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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

Michael Gilleland, Some Self-Similar Integer Sequences

FORMULA

a(n) = A000120(n-1) + 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(n-1).count('1') + 1

print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Dec 16 2021

(PARI) a(n) = hammingweight(n-1) + 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

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Last modified December 5 14:51 EST 2022. Contains 358588 sequences. (Running on oeis4.)