|
| |
|
|
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
|
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
|
|
|
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
|
| |
|
|
