OFFSET
0,2
COMMENTS
For n > 0: a(n) = A003314(n+1) - A003314(n) = A123753(n) - A123753(n-1). - Reinhard Zumkeller, Oct 12 2006
For k >= 2, k appears 2^(k-2) times consecutively. - Bernard Schott, Jun 08 2019
Also length of binary representation of 2n. - Michel Marcus, Oct 28 2020
FORMULA
Let b(1)=1, b(n) = a(n-floor(n/2)) + 1, then a(n) = b(n+1). - Benoit Cloitre, Oct 23 2002
G.f.: 1/(1-x) * (1 + Sum_{k>=0} x^2^k). - Ralf Stephan, Apr 15 2002
a(n) = ceiling(log_2(n+1)) + 1 = A029837(n+1) + 1. - Ralf Stephan, Apr 15 2002
a(n) = ceiling(average of previous entries) + 1. - Jon Perry, Apr 04 2004
MATHEMATICA
Table[IntegerLength[n, 2], {n, 1, 201, 2}] (* Harvey P. Dale, May 17 2011 *)
PROG
(PARI) a(n)=length(binary(2*n+1))
(Python)
def A070941(n): return n.bit_length()+1 # Chai Wah Wu, Mar 29 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 18 2002
STATUS
approved