A118655 Numbers k such that Hamming weight of k equals Hamming weight of k^3.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 56953, 65536, 113906, 131072, 227812, 262144, 455624, 524288, 911248, 1048576, 1822496, 1830651, 2097152, 3644992, 3661302, 4194304, 5502457, 7289984, 7322604

Offset: 1

Author

R. J. Mathar, May 18 2006

Keywords

• easy
• base
• nonn

Comments

A000079(n) is a subsequence because the Hamming weight of any A000079(n) is 1 and cubing such a number just adds binary zeros. A077436 is the sequence when the a(n) is squared, not cubed as here.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..177 (terms <= 2^40)

Crossrefs

Cf. A077436, A000079, A000120.

Programs

Mathematica

Select[Range[10^6], DigitCount[#, 2, 1] == DigitCount[#^3, 2, 1] &] (* Amiram Eldar, Jul 16 2023 *)

PARI

bitcnt(n)= { local(bitv,bitl) ; bitv=binary(n) ; bitvl=matsize(bitv) ; return(sum(i=1,bitvl[2],bitv[i])) ; }
{ for(i=1,8000000, if(bitcnt(i)==bitcnt(i^3), print1(i,",") ; ) ; ) ; }

Formula

A000120(a(n)) = A000120(a(n)^3).