A178745 - OEIS

%I #15 May 08 2018 15:11:56

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

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

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

%N Decimal expansion of Sum_{k>=1} 1/2^Partition(k).

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy], p. 836.

%e 0.9145815381782540637312161729442303697350532871815358384788470827...

%t s = 0; k = 1; While[k < 10000, s = N[s + 1/2^PartitionsP[k], 128]; k++ ]; s

%t RealDigits[NSum[1/2^PartitionsP[k],{k,\[Infinity]}, WorkingPrecision-> 200], 10,120][[1]] (* _Harvey P. Dale_, Mar 31 2018 *)

%Y Cf. A000041.

%K nonn,cons

%O 0,1

%A _Robert G. Wilson v_, Jun 08 2010

%E Edited by _N. J. A. Sloane_, Jun 08 2010