A092391 - OEIS

%I #62 Sep 05 2024 15:34:56

%S 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,

%T 28,29,31,31,33,34,36,33,35,36,38,38,40,41,43,42,44,45,47,47,49,50,52,

%U 50,52,53,55,55,57,58,60,59,61,62,64,64,66,67,69,65,67,68,70,70,72,73,75

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

%H Reinhard Zumkeller and Donovan Johnson, <a href="/A092391/b092391.txt">Table of n, a(n) for n = 0..10000</a> (terms up to a(1023) from Reinhard Zumkeller)

%H Max A. Alekseyev and N. J. A. Sloane, <a href="https://arxiv.org/abs/2112.14365">On Kaprekar's Junction Numbers</a>, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

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

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

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

%t Table[n + Total[IntegerDigits[n, 2]], {n, 0, 100}] (* _Jean-François Alcover_, Sep 03 2013 *)

%o (Haskell) a092391 n = n + a000120 n  -- _Reinhard Zumkeller_, May 13 2012

%o (PARI) A092391(n)=n+hammingweight(n) \\ _M. F. Hasler_, Oct 05 2013

%o (Python)

%o def a(n): return n + bin(n).count("1")

%o print([a(n) for n in range(72)]) # _Michael S. Branicky_, May 26 2022

%Y 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.

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

%Y Cf. A228088, A230091, A227915, A230300.

%K nonn,base

%O 0,2

%A _Reinhard Zumkeller_, May 08 2004