A192085 Number of ones in the binary expansion of n^3.

0, 1, 1, 4, 1, 6, 4, 6, 1, 6, 6, 6, 4, 5, 6, 8, 1, 6, 6, 8, 6, 6, 6, 9, 4, 7, 5, 8, 6, 9, 8, 10, 1, 6, 6, 11, 6, 10, 8, 12, 6, 8, 6, 9, 6, 11, 9, 10, 4, 9, 7, 7, 5, 8, 8, 10, 6, 10, 9, 7, 8, 11, 10, 12, 1, 6, 6, 11, 6, 9, 11, 11, 6, 13, 10, 14, 8, 13, 12, 13

Offset

0,4

Comments

The binary weight of n^3.

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Index entries for sequences related to binary expansion of n

Formula

a(n) = A000120(A000578(n)).

a(n) = [x^(n^3)] (1/(1 - x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Mar 27 2018

Maple

A192085 := proc(n) return add(b, b=convert(n^3, base, 2)): end: seq(A192085(n), n=0..100); # Nathaniel Johnston, Jun 23 2011

Prog

(Magma) [&+Intseq(n^3, 2): n in [0..79]];  // Bruno Berselli, Jun 24 2011
(Python)
def A192085(n):
....return bin(n**3).count('1') # Chai Wah Wu, Sep 03 2014
(PARI) a(n)=hammingweight(n^3) \\ Charles R Greathouse IV, Sep 27 2016

Crossrefs

Cf. A000120, A000578, A007088, A159918.

Sequence in context: A249074 A021710 A127555 * A117001 A206787 A327419

Adjacent sequences: A192082 A192083 A192084 * A192086 A192087 A192088

Keyword

nonn,base,easy

Author

Carl R. White, Jun 23 2011

Status

approved