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

0,2

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, 2022 (to appear).

Index entries for Colombian or self numbers and related sequences

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

Mathematica

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

Prog

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

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.

Sequence in context: A023838 A246795 A089625 * A187322 A335429 A156899

Adjacent sequences: A092388 A092389 A092390 * A092392 A092393 A092394

Keyword

nonn,base

Author

Reinhard Zumkeller, May 08 2004

Status

approved