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%I #24 Aug 31 2015 20:24:42
%S 9,17,33,49,50,65,73,77,85,86,97,106,129,137,149,157,161,165,178,186,
%T 193,201,212,213,225,226,257,265,273,279,281,285,300,305,307,310,317,
%U 321,325,332,334,345,355,365,366,378,385,393,394,413,426,427,449,469
%N Numbers n where n^2 is an anagram of (n+1)^2 in base 2.
%C Base 2 equivalent of A072841.
%C It appears that one of these numbers has a 1/n chance of being divisible by an odd number n, but a smaller than 1/n chance if n is even.
%H Charles R Greathouse IV, <a href="/A260477/b260477.txt">Table of n, a(n) for n = 1..10000</a>
%e 17 is a term of the sequence because its square base 2 (100100001) and 18's square base 2 (101000100) are anagrams.
%t For[i = 1, i <= 10000, i++,
%t If[Sort[IntegerDigits[i^2, 2]] == Sort[IntegerDigits[(i + 1)^2, 2]],
%t Print[i]]]
%o (PARI) is(n)=hammingweight(n^2)==hammingweight((n+1)^2) && #binary(n^2)==#binary((n+1)^2) \\ _Charles R Greathouse IV_, Aug 29 2015
%K base,easy,nonn
%O 1,1
%A _Dhilan Lahoti_, Aug 28 2015
%E a(27)-a(54) from _Charles R Greathouse IV_, Aug 29 2015
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