

A063787


a(2^k) = k + 1 and a(2^k + i) = 1 + a(i) for k >= 0 and 0 < i < 2^k.


21



1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..105.
Michael Gilleland, Some SelfSimilar Integer Sequences


FORMULA

a(n) = A000120(n1) + 1.
a(n) = log(A131136)/log(2).  Stephen Crowley, Aug 25 2008
a(n) = A007814(n) + A000120(n).  Gary W. Adamson, Jun 04 2009
a(n) = A000120(A086799(n)).  Reinhard Zumkeller, Jul 31 2010
a(n) = A000120(A047457(n)1) = A000120(A047457(n)+1).  Ilya Lopatin, Mar 16 2014


EXAMPLE

k = 3: a(2^3) = a(8) = 4 = 3 + 1.
k = 3, i = 5: a(2^3 + 5) = a(13) = 3 = 1 + 2 = 1 + a(5).
From Omar E. Pol, Jun 12 2009: (Start)
Triangle begins:
1;
2,2;
3,2,3,3;
4,2,3,3,4,3,4,4;
5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5;
6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6;
7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,...
(End)


PROG

(Python)
def a(n): return bin(n1).count('1') + 1
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Dec 16 2021
(PARI) a(n) = hammingweight(n1) + 1; \\ Michel Marcus, Nov 23 2022


CROSSREFS

Cf. A000079, A000120, A007814, A086799, A047457, A131136.
Cf. A330038 (partial sums).
Sequence in context: A211100 A329326 A105264 * A307092 A335458 A335454
Adjacent sequences: A063784 A063785 A063786 * A063788 A063789 A063790


KEYWORD

nonn,changed


AUTHOR

Reinhard Zumkeller, Aug 16 2001


STATUS

approved



