A008775 -id:A008775 - cp's OEIS frontend

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

Ralf Stephan, Dec 21 2004

nonn

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]

			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 + ...

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

Cf. A000182, A007814.

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

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

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

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

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

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.

A076417 Decimal expansion of first solution of equation cos(x)*cosh(x) = -1.

Original entry on oeis.org

1, 8, 7, 5, 1, 0, 4, 0, 6, 8, 7, 1, 1, 9, 6, 1, 1, 6, 6, 4, 4, 5, 3, 0, 8, 2, 4, 1, 0, 7, 8, 2, 1, 4, 1, 6, 2, 5, 7, 0, 1, 1, 1, 7, 3, 3, 5, 3, 1, 0, 6, 9, 9, 8, 8, 2, 4, 5, 4, 1, 3, 7, 1, 3, 1, 0, 5, 6, 7, 9, 9, 5, 2, 8, 4, 0, 4, 2, 8, 6, 3, 8, 5, 2, 6, 5, 6, 6, 5, 5, 0, 5, 8, 1, 8, 8, 6, 0, 3, 7, 0, 8, 4, 1, 0

Offset: 1

Zak Seidov, Oct 10 2002

This is an equation related to a cantilever beam: cos(x)*cosh(x) = -1. The first three solutions are: 1.875 (this sequence), 4.69409 (A076418) and 7.854757 (A076419).

			1.87510406871196116644530824107821416257011173353...

Z. Guede, I. Elishakov, A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure, Chaos, Solitons and Fractals 12 (7) (2001) 1267-1298.

Cf. A009398, A076418, A076419.

Cf. A005981, A058258, A008775.

RealDigits[x/.FindRoot[Cos[x]Cosh[x]==-1,{x,1.8}, WorkingPrecision->120], 10,120][[1]] (* Harvey P. Dale, Jul 24 2011 *)

solve(x=1, 2, cos(x)*cosh(x) + 1) \\ Michel Marcus, Sep 11 2019

cp's OEIS Frontend

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

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