Blum integer: Difference between revisions
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</syntaxhighlight>
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
{{Works with|jq}}
<syntaxhighlight lang=jq>
### Generic utilities
def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;
# tabular print
def tprint(columns; wide):
reduce _nwise(columns) as $row ("";
. + ($row|map(lpad(wide)) | join(" ")) + "\n" );
### Primes
def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else sqrt as $s
| 23
| until( . > $s or ($n % . == 0); . + 2)
| . > $s
end;
def primes: 2, (range(3;infinite;2) | select(is_prime));
# input: the number to be tested
def isprime($smalls):
if . < 2 then false
else sqrt as $s
| (first( $smalls[] as $p
| if . == $p then 1
elif . % $p == 0 then 0
elif $p > $s then 1
else empty
end) // null) as $result
| if $result then $result == 1
else ($smalls[-1] + 2)
| until( . > $s or ($n % . == 0); . + 2)
| . > $s
end
end;
# Assumes n is odd.
def firstPrimeFactor:
if (. == 1) then 1
elif (. % 3 == 0) then 3
elif (. % 5 == 0) then 5
else . as $n
| [4, 2, 4, 2, 4, 6, 2, 6] as $inc
| { k: 7,
i: 0 }
| ($n | sqrt) as $s
| until (.k > $s or .done;
if $n % .k == 0
then .done = true
else .k += $inc[.i]
| .i = (.i + 1) % 8
end )
| if .done then .k else $n end
end ;
### Blum integers
# Number of small primes to pre-compute
def task($numberOfSmallPrimes):
[limit($numberOfSmallPrimes; primes)] as $smalls
| { blum: [],
bc:0,
counts: { "1": 0, "3": 0, "7": 0, "9": 0 },
i: 1 }
| label $out
| foreach range(0; infinite) as $_ (.;
(.i|firstPrimeFactor) as $p
| .j = null
| if ($p % 4 == 3)
then (.i / $p) as $q
| if $q != $p and ($q % 4 == 3) and ($q | isprime($smalls))
then if (.bc < 50) then .blum[.bc] = .i else . end
| .counts[(.i % 10) | tostring] += 1
| .bc += 1
| .j = .i
else .
end
else .
end
| .i |= if (. % 5 == 3) then . + 4 else . + 2 end;
select(.j)
| if (.bc == 50)
then "First 50 Blum integers:",
(.blum | tprint(10; 3) )
elif .bc == 26828 or .bc % 1e5 == 0
then "The \(.bc) Blum integer is: \(.j)",
if .bc == 400000
then "\n% distribution of the first 400,000 Blum integers:",
((.counts|keys_unsorted[]) as $k
| " \( .counts[$k] / 4000 )% end in \($k)"),
break $out
else empty
end
else empty
end);
task(10000)
</syntaxhighlight>
{{output}}
<pre>
First 50 Blum integers:
21 33 57 69 77 93 129 133 141 161
177 201 209 213 217 237 249 253 301 309
321 329 341 381 393 413 417 437 453 469
473 489 497 501 517 537 553 573 581 589
597 633 649 669 681 713 717 721 737 749
The 26828 Blum integer is: 524273
The 100000 Blum integer is: 2075217
The 200000 Blum integer is: 4275533
The 300000 Blum integer is: 6521629
The 400000 Blum integer is: 8802377
% distribution of the first 400,000 Blum integers:
25.00125% end in 1
25.01675% end in 3
24.99725% end in 7
24.98475% end in 9
</pre>
=={{header|Julia}}==
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