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Decimal expansion of Sum_{n>=0} 1/(n*2^n + 1).
1

%I #19 Feb 13 2021 15:05:36

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

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

%U 2,6,6,3,3,2,2,3,7,5,9,7,6,7,6,5,1,9,8,4

%N Decimal expansion of Sum_{n>=0} 1/(n*2^n + 1).

%C This constant is the sum of reciprocals of Cullen numbers.

%F Equals Sum_{n>=0} 1/A002064(n).

%e 1.5106374481309548528461974960802456940320940529869241186970756482342266...

%t First[RealDigits[NSum[1/(n*2^n+1), {n, 0, Infinity}, NSumTerms -> 100, Method -> {"NIntegrate", "MaxRecursion" -> 10}, WorkingPrecision -> 100]]] (* _Stefano Spezia_, Jan 24 2021 *)

%o (PARI) suminf(n=0, 1/(n*2^n + 1)) \\ _Michel Marcus_, Jan 24 2021

%Y Cf. A002064.

%K nonn,cons

%O 1,2

%A _Marco RipĂ _, Jan 23 2021