A138597 -id:A138597 - cp's OEIS frontend

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

Zhao Hui Du, Jun 23 2023

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

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

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.

Cf. A000120, A192085, A138597 (equality).

Cf. A094694 (for squares).

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

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

A364785 Primes whose binary representation has more 1-bits than its cube.

Original entry on oeis.org

445317119867, 28498383073019, 114304774692347, 7594322375176157

Offset: 1

Martin Ehrenstein, Aug 07 2023

			445317119867 is a term because it is a prime number and A000120(445317119867) = 31, while A192085(445317119867) = A000120(445317119867^3) = 30.

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

Intersection of A363799 and A000040.

Cf. A000120, A192085, A138597.

cp's OEIS Frontend

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

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