A100126 Decimal expansion of Sum_{n>0} n/(prime(n)!).
8, 5, 9, 1, 2, 7, 1, 1, 0, 3, 5, 1, 0, 8, 8, 4, 3, 0, 3, 6, 8, 2, 2, 8, 2, 6, 2, 3, 0, 7, 5, 3, 7, 9, 0, 8, 2, 5, 8, 5, 3, 4, 5, 7, 7, 0, 6, 1, 7, 7, 6, 1, 7, 5, 6, 6, 1, 6, 7, 6, 1, 7, 7, 5, 8, 6, 8, 3, 7, 3, 2, 7, 9, 8, 0, 3, 7, 3, 5, 8, 8, 9, 7, 5, 1, 3, 2, 2, 0, 2, 2, 4, 8, 2, 6, 2, 5, 6, 3, 9
Offset: 0
Examples
0.8591271103510884303682282623075379082585345770617761756616761775868373279803735889751322022482625639...
Programs
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Mathematica
RealDigits[Total[Table[n/Prime[n]!,{n,20}]],10,120][[1]] (* Harvey P. Dale, Oct 26 2015 *)
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PARI
default(realprecision,100);sum(n=1,100,n/(prime(n)!),0.)