A340315 Decimal expansion of sum of reciprocals of A000111(n) (where A000111(n) is the n-th Euler or up/down number).

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

Offset: 1

Author

Marco Ripà, Jan 04 2021

Keywords

• nonn
• cons

Comments

The series 1/1 + 1/1 + 1/1 + 1/2 + 1/5 + 1/16 + 1/61 + 1/272 + 1/1385 + 1/7936 + ... converges to 3.783440983500797666683...

Examples

			3.783440983500797666683...
		

Crossrefs

Cf. A000111, A001250, A173253.

Programs

PARI

f(n)=if(n, 2*abs(polylog(-n, I)), 1); \\ A000111
suminf(n=0, 1/f(n)) \\ Michel Marcus, Jan 04 2021

Formula

Equals Sum_{k>=0} 1/A000111(k).

Extensions

More digits from Alois P. Heinz, Jan 06 2021