A348333 Decimal expansion of Sum_{n=-oo..oo} 1/(n^2)!.

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

Offset: 1

Author

Jianing Song, Oct 13 2021

Keywords

• nonn
• cons

Comments

This constant is irrational. The proof is similar to the one that e is irrational. Is this constant transcendental?

Examples

			3.083338844797273...
		

Crossrefs

Cf. A195907, A001113 (e = Sum_{n>=0} 1/n!).

Programs

Mathematica

RealDigits[N[1 + 2 *Sum[1/(n^2)!, {n, 1, Infinity}], 90]][[1]] (* Amiram Eldar, Oct 14 2021 *)

PARI

1 + 2*suminf(n=1, 1/(n^2)!)