A101921 - OEIS

%I #31 Apr 15 2023 01:51:16

%S 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,

%T 49,52,52,56,57,60,57,64,65,68,68,72,73,76,75,80,81,84,84,88,89,92,90,

%U 96,97,100,100,104,105,108,107,112,113,116,116,120,121,124,120,128

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

%C Exponent of 2 in tangent numbers A000182.

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

%C Also, exponent of 2 in 4^(n-1)/n. [_David Brink_, Aug 08 2013]

%H Iain Fox, <a href="/A101921/b101921.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%e 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 + ...

%t a[n_]:= If[n<1, 0, 2n -2 - IntegerExponent[n, 2]]; (* _Michael Somos_, Mar 02 2014 *)

%o (PARI) a(n)=valuation(4^(n-1)/n,2); \\ _Joerg Arndt_, Aug 13 2013

%o (Sage) [2*n-2 -valuation(n,2) for n in (1..100)] # _G. C. Greubel_, Nov 29 2021

%o (Python)

%o def A101921(n): return (n-1<<1)-(~n & n-1).bit_length() # _Chai Wah Wu_, Apr 14 2023

%Y Cf. A000182, A007814.

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

%K nonn

%O 1,3

%A _Ralf Stephan_, Dec 21 2004