A363799 Numbers whose binary representation has more 1-bits than its cube.

407182835067, 445317119867, 478351981947, 814365670134, 873268508637, 890634239734, 956703963894, 956703964539, 1628731340268, 1746537017274, 1781268479468, 1913407927788, 1913407929078, 2774213097787, 3257462680536, 3493074034548, 3562536958936, 3573277243773

Offset

1,1

Comments

a(n) must have more 1-bits than a(n)^3 when they are written in binary.

Links

Table of n, a(n) for n=1..18.

Chris K. Caldwell and G. L. Honaker, Jr., 445317119867, Prime Curios!

K. G. Hare, S. Laishram, and T. Stoll, Stolarsky's conjecture and the sum of digits of polynomial values, arXiv:1001.4169 [math.NT], 2010. See p. 3.

Thomas Stoll, On Stolarsky's conjecture: The sum of digits of n and n^h, Slides, 2010.

Example

407182835067 is a term because A000120(407182835067) = 29, while A192085(407182835067) = A000120(407182835067^3) = 28.

Prog

(PARI) isok(k) = hammingweight(k) > hammingweight(k^3); \\ Michel Marcus, Aug 07 2023

Crossrefs

Cf. A000120, A192085, A138597 (equality).

Cf. A094694 (for squares).

Sequence in context: A269417 A281963 A357687 * A082411 A113952 A218865

Adjacent sequences: A363796 A363797 A363798 * A363800 A363801 A363802

Keyword

nonn,base

Author

Zhao Hui Du, Jun 23 2023

Extensions

a(9)-a(18) from Martin Ehrenstein, Jul 31 2023

Status

approved