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Decimal expansion of the sum of reciprocals of the strict partition function (the function giving the number of partitions of an integer into distinct parts).
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%I #47 May 25 2023 08:10:02

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

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

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

%N Decimal expansion of the sum of reciprocals of the strict partition function (the function giving the number of partitions of an integer into distinct parts).

%C Conjecture: This number is transcendental. - _Zhi-Wei Sun_, May 24 2023

%H Vaclav Kotesovec, <a href="/A237515/b237515.txt">Table of n, a(n) for n = 1..750</a> (terms 1..100 from Jean-Francois Alcover)

%F Sum_{n>=1} 1/A000009(n). - _Vaclav Kotesovec_, Dec 08 2015

%e 4.6734445793163451750334174346113053985897...

%t digits = 100; NSum[1/PartitionsQ[n], {n, 1, Infinity}, NSumTerms -> 15000, WorkingPrecision -> digits+1] // RealDigits[#, 10, digits]& // First

%Y Cf. A000009, A078506, A303662.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Feb 24 2014