A090003 Length of longest contiguous block of 1's in binary expansion of n^3.

0, 1, 1, 2, 1, 5, 2, 3, 1, 2, 5, 2, 2, 1, 3, 4, 1, 2, 2, 2, 5, 2, 2, 5, 2, 4, 1, 3, 3, 5, 4, 5, 1, 2, 2, 4, 2, 3, 2, 4, 5, 3, 2, 2, 2, 6, 5, 4, 2, 3, 4, 2, 1, 2, 3, 4, 3, 2, 5, 2, 4, 3, 5, 6, 1, 2, 2, 2, 2, 4, 4, 3, 2, 5, 3, 8, 2, 4, 4, 4, 5, 6, 3, 3, 2, 4, 2, 3, 2, 3, 6, 8, 5, 2, 4, 5, 2, 4, 3, 3, 4, 5

Offset: 0

Author

Reinhard Zumkeller, Nov 20 2003

Keywords

• nonn
• base

Comments

a(n) = A038374(A000578(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A090001, A090002, A090049.

Programs

Mathematica

Join[{0},Table[Max[Length/@Select[Split[IntegerDigits[n^3,2]],MemberQ[#,1]&]],{n,110}]] (* Harvey P. Dale, Aug 28 2016 *)

PARI

A038374(n) = { if(n<2, return(n)); n>>=valuation(n, 2); if(n<2, return(n)); my(e=valuation(n+1, 2)); max(e, A038374(n>>e)); } \\ After Charles R Greathouse IV, Jan 12 2014
A090003(n) = A038374(n^3); \\ Antti Karttunen, Jul 09 2017