A135560 a(n) = A007814(n) + A036987(n-1) + 1.

2, 3, 1, 4, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 8, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1

Offset: 1

Author

N. J. A. Sloane, Mar 01 2008

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A036987, A091090, A135534, A135561.

Programs

Mathematica

a[n_] := 1 + IntegerExponent[n, 2] + Sum[(-1)^(n - k - 1)*Binomial[n - 1, k]* Sum[Binomial[k, 2^j - 1], {j, 0, k}], {k, 0, n - 1}]; Table[a[n], {n, 1, 25}] (* G. C. Greubel, Oct 17 2016 *)

PARI

a(n)=my(t=valuation(n, 2)); t + (n==2^t) + 1 \\ Charles R Greathouse IV, Oct 17 2016

Python

def A135560(n): return (m:=(~n & n-1)).bit_length()+int(m==n-1)+1 # Chai Wah Wu, Jul 06 2022

Formula

a(2^k) = k+2; a(2^k + 2^(k-1)) = k. - Reinhard Zumkeller, Mar 02 2008

Extensions

More terms from Reinhard Zumkeller, Mar 02 2008