|
%I #31 Aug 07 2023 12:28:30
%S 407182835067,445317119867,478351981947,814365670134,873268508637,
%T 890634239734,956703963894,956703964539,1628731340268,1746537017274,
%U 1781268479468,1913407927788,1913407929078,2774213097787,3257462680536,3493074034548,3562536958936,3573277243773
%N Numbers whose binary representation has more 1-bits than its cube.
%C a(n) must have more 1-bits than a(n)^3 when they are written in binary.
%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=445317119867">445317119867</a>, Prime Curios!
%H K. G. Hare, S. Laishram, and T. Stoll, <a href="https://arxiv.org/abs/1001.4169">Stolarsky's conjecture and the sum of digits of polynomial values</a>, arXiv:1001.4169 [math.NT], 2010. See p. 3.
%H Thomas Stoll, <a href="https://www.irif.fr/~steiner/stoll_aussois.pdf">On Stolarsky's conjecture: The sum of digits of n and n^h</a>, Slides, 2010.
%e 407182835067 is a term because A000120(407182835067) = 29, while A192085(407182835067) = A000120(407182835067^3) = 28.
%o (PARI) isok(k) = hammingweight(k) > hammingweight(k^3); \\ _Michel Marcus_, Aug 07 2023
%Y Cf. A000120, A192085, A138597 (equality).
%Y Cf. A094694 (for squares).
%K nonn,base
%O 1,1
%A _Zhao Hui Du_, Jun 23 2023
%E a(9)-a(18) from _Martin Ehrenstein_, Jul 31 2023
| 