A101921 a(2n) = a(n) + 2n - 1, a(2n+1) = 4n.

0, 1, 4, 4, 8, 9, 12, 11, 16, 17, 20, 20, 24, 25, 28, 26, 32, 33, 36, 36, 40, 41, 44, 43, 48, 49, 52, 52, 56, 57, 60, 57, 64, 65, 68, 68, 72, 73, 76, 75, 80, 81, 84, 84, 88, 89, 92, 90, 96, 97, 100, 100, 104, 105, 108, 107, 112, 113, 116, 116, 120, 121, 124, 120, 128

Offset: 1

Author

Ralf Stephan, Dec 21 2004

Keywords

• nonn

Comments

Exponent of 2 in tangent numbers A000182.

Also, exponent of 2 in the sequences A008775, A009670, A009764, A009798, A012227, A024236, A024277, A024299, A052510.

Also, exponent of 2 in 4^(n-1)/n. [David Brink, Aug 08 2013]

Examples

			G.f. = x^2 + 4*x^3 + 4*x^4 + 8*x^5 + 9*x^6 + 12*x^7 + 11*x^8 + 16*x^9 + 17*x^10 + ...
		

Links

• Iain Fox, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000182, A007814.

Cf. A008775, A009670, A009764, A009798, A012227, A024236, A024277, A024299, A052510.

Programs

Mathematica

a[n_]:= If[n<1, 0, 2n -2 - IntegerExponent[n, 2]]; (* Michael Somos, Mar 02 2014 *)

PARI

a(n)=valuation(4^(n-1)/n,2); \\ Joerg Arndt, Aug 13 2013

Python

def A101921(n): return (n-1<<1)-(~n & n-1).bit_length() # Chai Wah Wu, Apr 14 2023

Sage

[2*n-2 -valuation(n,2) for n in (1..100)] # G. C. Greubel, Nov 29 2021

Formula

a(n) = 2n - 2 - A007814(n).

a(n) = A007814(A000182(n)).

G.f.: Sum_{k>=0} t^2*(1+4*t+t^2)/(1-t^2)^2 where t=x^2^k.