A369500 - OEIS

%I #8 Jan 25 2024 03:58:12

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

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

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

%N Decimal expansion of Sum_{k=-oo..oo} 1/(2^(k/2)+2^(-k/2)).

%C Larger than Pi/log(2) by less than 10^(-11).

%H Gérard Maze and Lorenz Minder, <a href="https://doi.org/10.4171/em/61">A new family of almost identities</a>, Elemente der Mathematik, Vol. 62, No. 3 (2007), pp. 89-97.

%F Equals (Pi/log(2)) * (1 + 2 * Sum_{k>=1} sech(2*k*Pi^2/log(2))).

%e 4.5323601418349687021424689879289647378697386773791184248...

%t RealDigits[Chop[N[Sum[1/(2^(k/2) + 2^(-k/2)), {k, -Infinity, Infinity}], 120]]][[1]]

%o (PARI) (Pi/log(2)) * (1 + 2 * sumpos(k = 1, 1/cosh(2*k*Pi^2/log(2))))

%Y Cf. A163973.

%K nonn,cons

%O 1,1

%A _Amiram Eldar_, Jan 25 2024