A092391 a(n) = n + wt(n), where wt(n) = A000120(n) = binary weight of n.

0, 2, 3, 5, 5, 7, 8, 10, 9, 11, 12, 14, 14, 16, 17, 19, 17, 19, 20, 22, 22, 24, 25, 27, 26, 28, 29, 31, 31, 33, 34, 36, 33, 35, 36, 38, 38, 40, 41, 43, 42, 44, 45, 47, 47, 49, 50, 52, 50, 52, 53, 55, 55, 57, 58, 60, 59, 61, 62, 64, 64, 66, 67, 69, 65, 67, 68, 70, 70, 72, 73, 75

Offset: 0

Author

Reinhard Zumkeller, May 08 2004

Keywords

• nonn
• base

Links

• Reinhard Zumkeller and Donovan Johnson, Table of n, a(n) for n = 0..10000 (terms up to a(1023) from Reinhard Zumkeller)
• Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.
• Index entries for Colombian or self numbers and related sequences

Crossrefs

A010061 gives the numbers not occurring in this sequence. A228082 gives the terms of this sequence sorted into ascending order, with duplicates removed. A228085(n) gives the number of times n occurs in this sequence.

Cf. A000120, A228083, A228086, A228087, A228091, A011371, A230058, A230092, A062028.

Cf. A228088, A230091, A227915, A230300.

Programs

Haskell

a092391 n = n + a000120 n  -- Reinhard Zumkeller, May 13 2012

Mathematica

Table[n + Total[IntegerDigits[n, 2]], {n, 0, 100}] (* Jean-François Alcover, Sep 03 2013 *)

PARI

A092391(n)=n+hammingweight(n) \\ M. F. Hasler, Oct 05 2013

Python

def a(n): return n + bin(n).count("1")
print([a(n) for n in range(72)]) # Michael S. Branicky, May 26 2022

Formula

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

A010062(n+1) = a(A010062(n)).

G.f.: (1/(1 - x))*Sum_{k>=0} (2^k + 1)*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jul 23 2017