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

%I A100127 #19 Mar 23 2025 18:40:26
%S A100127 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,
%T A100127 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,
%U A100127 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
%N A100127 Decimal expansion of Sum_{n>0} prime(n)/n!.
%C A100127 This constant is irrational (Erdős, 1958). - _Amiram Eldar_, Apr 13 2020
%H A100127 Paul Erdős, <a href="https://www.renyi.hu/~p_erdos/1958-19.pdf">Sur certaines séries à valeur irrationnelle</a> (in French), Enseignement Math. (2) 4 (1958), pp. 93-100.
%e A100127 4.73863870268621999271779470348124955360182384664210664248096193484375408779697167489...
%t A100127 RealDigits[ Sum[ Prime[n]/n!, {n, 75}], 10, 105][[1]] (* _Robert G. Wilson v_, Jan 18 2015 *)
%o A100127 (PARI) default(realprecision,100);sum(n=1,100,prime(n)/(n!),0.)
%Y A100127 Cf. A094289, A100124, A100126.
%K A100127 cons,nonn
%O A100127 1,1
%A A100127 Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004