cp's OEIS Frontend

A345974 Decimal expansion of Sum_{k>=0} Product_{i=1..k} 1/(prime(i)-1).

%I A345974 #25 Jun 26 2025 07:57:54
%S A345974 2,6,4,8,1,0,1,7,5,9,7,0,1,4,7,1,0,2,3,3,7,0,8,8,4,1,4,5,3,6,0,6,4,7,
%T A345974 1,4,9,2,7,2,5,8,7,0,0,2,1,4,0,3,3,9,3,2,0,7,6,7,4,4,5,4,7,9,2,5,2,7,
%U A345974 4,0,4,6,1,6,2,6,4,2,4,7,5,8,9,3,8,1,7,0,0,7,6,8,2,8,7,3,2,0,8,1,0,9,5
%N A345974 Decimal expansion of Sum_{k>=0} Product_{i=1..k} 1/(prime(i)-1).
%H A345974 Peter Cameron, <a href="https://cameroncounts.wordpress.com/2021/05/23/a-new-constant/">A new constant?</a>, Blog Post, May 23 2021.
%H A345974 Peter Cameron, <a href="/A345974/a345974.png">A new constant?</a>, local copy of Blog Post, with permission.
%F A345974 Equals Sum_{k>=0} 1/A005867(k) = Sum_{k>=1} 1/A055932(k) = Sum_{k>=1} 1/A057335(k). - _Amiram Eldar_, Jun 26 2025
%e A345974 2.64810175970147102337088414536064714927258700214033932076744547925274...
%p A345974 c:= sum(product(1/(ithprime(i)-1), i=1..k), k=0..infinity):
%p A345974 evalf(c, 140);  # _Alois P. Heinz_, Jun 30 2021
%o A345974 (PARI) suminf(k=0,prod(i=1,k,1/(prime(i)-1)))
%Y A345974 Cf. A005867, A055932, A057335, A345965.
%K A345974 nonn,cons
%O A345974 1,1
%A A345974 _Hugo Pfoertner_, Jun 30 2021