A226121 Decimal expansion of sum_{n=1..infinity} n^3/(exp(2*Pi*n/13)-1).

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

Offset: 3

Author

Jean-François Alcover, May 27 2013

Keywords

• nonn
• cons

Comments

An almost-integer discovered by Simon Plouffe. The computed sum equals 119 within 31 digits after the decimal point.

Examples

			119.0000000000000000000000000000000959374585102554733558858491339738415043391...
		

Links

• Simon Plouffe, Simon Plouffe Home Page
• Eric Weisstein's MathWorld, Almost Integer

Crossrefs

Cf. A060295 (a famous almost-integer: Ramanujan's constant), A226120 (another surprising almost-integer by Simon Plouffe).

Programs

Mathematica

NSum[n^3/(Exp[2*Pi*n/13] - 1), {n, 1, Infinity}, NSumTerms -> 500,    WorkingPrecision -> 100] // RealDigits[#, 10, 100] & // First

Extensions

Offset corrected by Rick L. Shepherd, Jan 01 2014