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A261586
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Odd numbers n such that the sum of the binary digits of n equals the sum of the binary digits of n^2.
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3
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1, 3, 7, 15, 31, 63, 79, 91, 127, 157, 159, 183, 187, 255, 279, 287, 317, 319, 351, 365, 375, 379, 445, 511, 573, 575, 637, 639, 703, 735, 751, 759, 763, 815, 893, 975, 1023, 1071, 1087, 1145, 1149, 1151, 1215, 1255, 1277, 1279, 1407, 1449, 1455, 1463
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OFFSET
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1,2
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COMMENTS
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A077436 consists of elements of this sequence times powers of 2.
Hare, Laishram, & Stoll show that this sequence is infinite. In particular for each k in {12, 13, 16, 17, 18, 19, 20, ...} there are infinitely many terms in this sequence with binary digit sum k.
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LINKS
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EXAMPLE
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15 = 1111_2 and 15^2 = 11100001_2, both of which have a Hamming weight (sum of binary digits) equal to 4.
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MATHEMATICA
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Select[Range[1, 1463, 2], Total@ IntegerDigits[#, 2] == Total@ IntegerDigits[#^2, 2] &] (* Michael De Vlieger, Aug 29 2015 *)
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PROG
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(PARI) is(n)=n%2 && hammingweight(n)==hammingweight(n^2)
(Magma) [n: n in [1..1500 by 2] | &+Intseq(n, 2) eq &+Intseq(n^2, 2) ]; // Vincenzo Librandi, Aug 30 2015
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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