A100126 -id:A100126 - cp's OEIS frontend

A100127 Decimal expansion of Sum_{n>0} prime(n)/n!.

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

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004

This constant is irrational (Erdős, 1958). - Amiram Eldar, Apr 13 2020

			4.73863870268621999271779470348124955360182384664210664248096193484375408779697167489...

Paul Erdős, Sur certaines séries à valeur irrationnelle (in French), Enseignement Math. (2) 4 (1958), pp. 93-100.

Cf. A094289, A100124, A100126.

RealDigits[ Sum[ Prime[n]/n!, {n, 75}], 10, 105][[1]] (* Robert G. Wilson v, Jan 18 2015 *)

default(realprecision,100);sum(n=1,100,prime(n)/(n!),0.)

A100128 Decimal expansion of Sum_{n>0} 1/(n*prime(n)^n).

Original entry on oeis.org

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

Offset: 0

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004

			0.5583276222317691586142791968036046951752521282087420173902229174235854763316376176520093696726521040...

Cf. A094289, A100124, A100126, A100127.

PARI
```
suminf(k=1, 1/(k*prime(k)^k))
```

cp's OEIS Frontend

A100127 Decimal expansion of Sum_{n>0} prime(n)/n!.

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