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a(n) = smallest m such that value of odd harmonic series Sum_{j=0..m} 1/(2j+1) is >= n.
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%I #34 Sep 20 2020 00:42:23

%S 0,7,56,418,3091,22845,168803,1247297,9216353,68100150,503195828,

%T 3718142207,27473561357,203003686105,1500005624923,11083625711270,

%U 81897532160124,605145459495140,4471453748222756,33039822589391675

%N a(n) = smallest m such that value of odd harmonic series Sum_{j=0..m} 1/(2j+1) is >= n.

%H Vincenzo Librandi, <a href="/A092318/b092318.txt">Table of n, a(n) for n = 1..1000</a> (127 terms corrected by Gerhard Kirchner)

%F a(n) = floor(exp(2*n-gamma)/4+1/8), for all n > 1. - _M. F. Hasler_ and _Robert G. Wilson v_, Jan 22 2017

%F a(n) = floor(exp(2*n-gamma)/4), for all n > 1, see correction in A092315, _Gerhard Kirchner_, Jul 25 2020

%t a[n_] := Floor[(Exp[2 n - EulerGamma] + 1/2)/4]; a[1] = 0; Array[a, 20] (* _Robert G. Wilson v_, Jan 25 2017 *)

%o (PARI) A092318=n->floor(exp(2*n-Euler)/4+1/8)-(n<2) \\ Cf. comments in A092315. - _M. F. Hasler_, Jan 24 2017

%Y Apart from first term, same as A092315. Equals (A092317-1)/2.

%Y Cf. A074599, A025547.

%Y Cf. A281355 (= a(n) + 1) for a variant.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Feb 16 2004

%E More terms (computed from A092317) from _M. F. Hasler_, Jan 22 2017

%E a(17) corrected by _Gerhard Kirchner_, Jul 26 2020