A249154 (n+1) times the number of 1's in the binary expansion of n.

0, 2, 3, 8, 5, 12, 14, 24, 9, 20, 22, 36, 26, 42, 45, 64, 17, 36, 38, 60, 42, 66, 69, 96, 50, 78, 81, 112, 87, 120, 124, 160, 33, 68, 70, 108, 74, 114, 117, 160, 82, 126, 129, 176, 135, 184, 188, 240, 98, 150, 153, 208, 159, 216, 220, 280, 171, 232, 236, 300, 244, 310, 315, 384, 65

Offset: 0

Author

Antti Karttunen, Nov 02 2014

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A000788, A187059, A245788, A091512.

Programs

Mathematica

A249154[n_] := (n + 1)*DigitCount[n, 2, 1]; Array[A249154, 100, 0] (* Paolo Xausa, Feb 11 2025 *)

PARI

a(n) = (n+1)*hammingweight(n); \\ Michel Marcus, Feb 11 2025

Python

def A249154(n): return (n+1)*n.bit_count() # Chai Wah Wu, Nov 11 2024

Scheme

(define (A249154 n) (* (+ n 1) (A000120 n)))

Formula

a(n) = (n+1) * A000120(n).

a(n) = A000120(n) + A245788(n).

a(n) = 2*A000788(n) - A187059(n).