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Rare numbers: Difference between revisions
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75 8,320,411,466,598,809,138 19: 00:12:48.590 00:15:14.316
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=={{header|J}}==
The following function determines whether a given integer is "rare", as can be seen in the sample output.
To use it to find rare numbers, one would simply apply it to each integer seriatim, and keep the numbers where its output is true (I.@:rare i. AS_HIGH_AS_YOU_WANT_TO_CHECK); but since these numbers are, well, rare, actually doing so would take a very long time.
<lang j>rare =: ( np@:] *. (nbrPs rr) ) b10
np =: -.@:(-: |.) NB. Not palindromic
nbrPs =: > *. sdPs NB. n is Bigger than R and the perfect square constraint is satisfied
sdPs =: + *.&:ps - NB. n > rr and both their sum and difference are perfect squares
ps =: 0 = 1 | %: NB. Perfect square (integral sqrt)
rr =: 10&#.@:|. NB. Do note we do reverse the digits twice (once here, once in np)
b10 =: 10&#.^:_1 NB. Base 10 digits</lang>
{{out}}
<lang j> NB. From OEIS
R =: 65 621770 281089082 2022652202 2042832002 868591084757 872546974178 872568754178 6979302951885 20313693904202 20313839704202 20331657922202 20331875722202 20333875702202 40313893704200
rare"0 R
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1</lang>
=={{header|Java}}==
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