cp's OEIS Frontend

A157701 Decimal expansion of 2*(14*sigma+5)/625 where sigma = sqrt(5)*log(golden ratio).

%I A157701 #12 May 15 2019 12:35:05
%S A157701 0,6,4,2,0,5,8,0,1,3,8,7,9,6,8,4,5,2,3,5,5,6,1,6,5,2,2,0,9,0,4,6,7,8,
%T A157701 0,7,6,4,7,5,5,1,9,1,6,4,4,4,5,1,2,4,4,1,3,3,2,7,8,4,6,8,3,6,4,7,1,6,
%U A157701 6,8,5,6,1,3,1,6,4,6,7,7,9,6,7,2,4,8,6,9,0,9,6,4,6,0,8,8,6,3,5,0,0,5,5,0,9
%N A157701 Decimal expansion of 2*(14*sigma+5)/625 where sigma = sqrt(5)*log(golden ratio).
%C A157701 The factor 28 in the Lehmer paper has been corrected to 14.
%C A157701 Equals sum_{n=1..infinity} (-1)^n*n^3/binomial(2n,n).
%H A157701 D. H. Lehmer, <a href="http://www.jstor.org/stable/2322496">Interesting series involving the Central Binomial Coefficient</a>, Am. Math. Monthly 92, no 7 (1985) 449-457.
%H A157701 R. J. Mathar, <a href="http://arxiv.org/abs/0905.0215">Corrigenda to "Interesting series involving..."</a>, arXiv:0905.0215
%H A157701 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A157701 Equals 2*(14*A002163*A002390+5)/625 .
%e A157701 0.064205801387968452355..
%p A157701 2/625*(14*sqrt(5)*log((1+sqrt(5))/2)+5) ;
%t A157701 Join[{0},RealDigits[2*(14*Sqrt[5]*Log[GoldenRatio]+5)/625,10,120][[1]]] (* _Harvey P. Dale_, Mar 13 2015 *)
%o A157701 (PARI) 2*(14*sqrt(5)*log((sqrt(5)+1)/2)+5)/625 \\ _Charles R Greathouse IV_, May 15 2019
%Y A157701 Cf. A145434, A145433.
%K A157701 cons,easy,nonn
%O A157701 0,2
%A A157701 _R. J. Mathar_, Mar 04 2009