A369500 Decimal expansion of Sum_{k=-oo..oo} 1/(2^(k/2)+2^(-k/2)).

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, 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, 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

Offset: 1

Author

Amiram Eldar, Jan 25 2024

Keywords

• nonn
• cons

Comments

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

Examples

			4.5323601418349687021424689879289647378697386773791184248...
		

Links

• Gérard Maze and Lorenz Minder, A new family of almost identities, Elemente der Mathematik, Vol. 62, No. 3 (2007), pp. 89-97.

Crossrefs

Cf. A163973.

Programs

Mathematica

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

PARI

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

Formula

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