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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. 20
 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 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 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 AUTHOR Reinhard Zumkeller, Aug 16 2001 STATUS approved

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Last modified June 29 10:16 EDT 2022. Contains 354912 sequences. (Running on oeis4.)