

A261586


Odd numbers n such that the sum of the binary digits of n equals the sum of the binary digits of n^2.


3



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

1,2


COMMENTS

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.
Subsequence of A077436.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
K. G. Hare, S. Laishram, and T. Stoll, The sum of digits of n and n^2, International Journal of Number Theory 7:7 (2011), pp. 17371752.
Giuseppe Melfi, On simultaneous binary expansions of n and n^2, arXiv:math/0402458 [math.NT], 2004.


EXAMPLE

15 = 1111_2 and 15^2 = 11100001_2, both of which have a Hamming weight (sum of binary digits) equal to 4.


MATHEMATICA

Select[Range[1, 1463, 2], Total@ IntegerDigits[#, 2] == Total@ IntegerDigits[#^2, 2] &] (* Michael De Vlieger, Aug 29 2015 *)


PROG

(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


CROSSREFS

Cf. A077436, A254066.
Sequence in context: A119407 A224521 A269167 * A043734 A151359 A147596
Adjacent sequences: A261583 A261584 A261585 * A261587 A261588 A261589


KEYWORD

nonn,base


AUTHOR

Charles R Greathouse IV, Aug 25 2015


STATUS

approved



