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</span><span class="RktMeta"></span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._min%29%29">min</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._max%29%29">max</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">pre-ticks</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" 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class="RktSym">digits</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">#f</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">pre-ticks</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29">define</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">linear-ticks/no-sc</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><span class="badlink"><span class="RktValLink">ticks</span></span></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><span class="badlink"><span class="RktValLink">linear-ticks-layout</span></span></span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">linear-ticks-format/no-sc</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><span class="badlink"><span class="RktValLink">plot-x-ticks</span></span></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">linear-ticks/no-sc</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;</span><span class="hspace"> </span><span class="RktCmt">almost</span><span class="hspace"> </span><span class="RktCmt">global</span><span class="hspace"> </span><span class="RktCmt">change</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><span class="badlink"><span class="RktValLink">plot-y-ticks</span></span></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">linear-ticks/no-sc</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktCmt">;</span><span class="hspace"> </span><span class="RktCmt">almost</span><span class="hspace"> </span><span class="RktCmt">global</span><span class="hspace"> </span><span class="RktCmt">change</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29">define</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">binary-reverse</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">x</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/let.html#%28form._%28%28lib._racket%2Fprivate%2Fletstx-scheme..rkt%29._let%29%29">let</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">loop</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">x</span><span class="RktMeta"></span><span class="hspace"> </span><span 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href="http://docs.racket-lang.org/reference/number-types.html#%28def._%28%28quote._~23~25kernel%29._zero~3f%29%29">zero?</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">x</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">r</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">loop</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._quotient%29%29">quotient</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">x</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">2</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2B%29%29">+</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2A%29%29">*</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">2</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">r</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._remainder%29%29">remainder</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">x</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">2</span><span class="RktPn">)</span><span class="RktPn">)</span><span 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class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/vectors.html#%28def._%28%28quote._~23~25kernel%29._vector%29%29">vector</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">i</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._-%29%29"><span class="nobreak">-</span></a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">i</span><span 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class="RktSym">prim</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/for.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._for%2Flist%29%29">for/list</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">i</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/sequences.html#%28def._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._in-range%29%29">in-range</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">1</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">65536</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:when</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/math/number-theory.html#%28def._%28%28lib._math%2Fnumber-theory..rkt%29._prime~3f%29%29">prime?</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">i</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/vectors.html#%28def._%28%28quote._~23~25kernel%29._vector%29%29">vector</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">i</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._-%29%29"><span class="nobreak">-</span></a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">i</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">binary-reverse</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">i</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/plot/plotting.html#%28def._%28%28lib._plot%2Fpict..rkt%29._plot%29%29">plot</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:title</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">"All</span><span class="hspace"> </span><span class="RktVal">vs</span><span class="hspace"> </span><span class="RktVal">Prime</span><span class="hspace"> </span><span class="RktVal">Paralelograms"</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/pairs.html#%28def._%28%28quote._~23~25kernel%29._list%29%29">list</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><span class="badlink"><span class="RktValLink">points</span></span></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">all</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:sym</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/quote.html#%28form._%28%28quote._~23~25kernel%29._quote%29%29">'</a></span><span class="RktSym">dot</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:color</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/quote.html#%28form._%28%28quote._~23~25kernel%29._quote%29%29">'</a></span><span class="RktSym">black</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:alpha</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">.1</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><span class="badlink"><span class="RktValLink">points</span></span></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">prim</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:sym</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/quote.html#%28form._%28%28quote._~23~25kernel%29._quote%29%29">'</a></span><span class="RktSym">dot</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:color</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/quote.html#%28form._%28%28quote._~23~25kernel%29._quote%29%29">'</a></span><span class="RktSym">blue</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:alpha</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">.5</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:x-label</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">"n"</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:y-label</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">"f(n)"</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:y-min</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">-32768</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:y-max</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">65536</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:x-min</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:width</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">400</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">#:height</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">600</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li></ol><p>=></p><blockquote><table style="font-size:90%;table-layout:fixed;width:100%;word-wrap:break-word"><tr><td><p><img alt="image" height="606" src="http://pasterack.org/98522.png" style="vertical-align: 0px; margin: -3px -3px -3px -3px;" width="406"/></p></td></tr></table></blockquote></div>
Plot of Prime Parallelograms
#lang
racket
;
https://gus-massa.blogspot.com.ar/2019/09/more-on-prime-parallelograms.html
(
require
math/number-theory
)
(
require
plot/pict
)
#;
(
plot-new-window?
#t
)
(
require
plot/utils
)
(
define
(
(
linear-ticks-format/no-sc
)
min
max
pre-ticks
)
(
define
digits
(
digits-for-range
min
max
)
)
(
map
(
lambda
(
pt
)
(
real->plot-label
(
pre-tick-value
pt
)
digits
#f
)
)
pre-ticks
)
)
(
define
(
linear-ticks/no-sc
)
(
ticks
(
linear-ticks-layout
)
(
linear-ticks-format/no-sc
)
)
)
(
plot-x-ticks
(
linear-ticks/no-sc
)
)
;
almost
global
change
(
plot-y-ticks
(
linear-ticks/no-sc
)
)
;
almost
global
change
(
define
(
binary-reverse
x
)
(
let
loop
(
[
x
x
]
[
r
0
]
)
(
if
(
zero?
x
)
r
(
loop
(
quotient
x
2
)
(
+
(
*
2
r
)
(
remainder
x
2
)
)
)
)
)
)
(
define
all
(
for/list
(
[
i
(
in-range
1
65536
)
]
)
(
vector
i
(
-
i
(
binary-reverse
i
)
)
)
)
)
(
define
prim
(
for/list
(
[
i
(
in-range
1
65536
)
]
#:when
(
prime?
i
)
)
(
vector
i
(
-
i
(
binary-reverse
i
)
)
)
)
)
(
plot
#:title
"All
vs
Prime
Paralelograms"
(
list
(
points
all
#:sym
'
dot
#:color
'
black
#:alpha
.1
)
(
points
prim
#:sym
'
dot
#:color
'
blue
#:alpha
.5
)
)
#:x-label
"n"
#:y-label
"f(n)"
#:y-min
-32768
#:y-max
65536
#:x-min
0
#:width
400
#:height
600
)
=>