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

%I #18 Feb 16 2025 08:33:19

%S 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,

%T 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,

%U 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

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

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

%H Simon Plouffe, <a href="http://www.plouffe.fr">Simon Plouffe Home Page</a>

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/AlmostInteger.html">Almost Integer</a>

%e 119.0000000000000000000000000000000959374585102554733558858491339738415043391...

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

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

%K nonn,cons,changed

%O 3,3

%A _Jean-François Alcover_, May 27 2013

%E Offset corrected by _Rick L. Shepherd_, Jan 01 2014