A354857 - OEIS

%I #5 Jun 09 2022 08:45:53

%S 6,1,4,0,7,1,5,3,6,6,1,4,3,6,2,8,1,3,6,0,3,6,3,6,0,8,3,6,4,7,6,0,1,6,

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

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

%N Decimal expansion of Sum_{k,m>=1} (-1)^(k+m+1)/floor(sqrt(k+m))^3.

%H Ovidiu Furdui, <a href="https://www.jstor.org/stable/10.4169/mathmaga.83.3.227a">Problem 1849</a>, Mathematics Magazine, Vol. 83, No. 3 (2010), p. 227; <a href="https://www.jstor.org/stable/10.4169/math.mag.84.3.229">An alternating double series</a>, Solution to Problem 1849 by Omran Kouba, ibid., Vol. 84, No. 3 (2010), pp. 234-235.

%F Equals Pi^2/12 + log(2) - 3*zeta(3)/4.

%e 0.61407153661436281360363608364760166961123536570828...

%t RealDigits[Pi^2/12 + Log[2] - 3*Zeta[3]/4, 10, 100][[1]]

%Y Cf. A002117, A002162, A072691, A197070.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Jun 09 2022