cp's OEIS Frontend

A338475 Decimal expansion of the sum of reciprocals of the smallest primes > 2^k for k >= 0.

%I A338475 #23 Nov 01 2020 08:11:32
%S A338475 1,2,4,0,4,0,7,1,4,6,6,5,5,9,6,0,6,2,8,9,4,6,4,1,8,0,2,1,4,0,5,7,2,8,
%T A338475 3,3,9,2,3,1,3,8,1,0,7,3,4,6,9,0,9,9,2,6,9,0,3,7,1,6,4,2,6,1,5,7,4,3,
%U A338475 0,0,2,2,7,5,6,2,1,2,7,2,3,9,6,4,4,7,4,0,1,9
%N A338475 Decimal expansion of the sum of reciprocals of the smallest primes > 2^k for k >= 0.
%C A338475 If q(k) = A014210(k) is the smallest prime > 2^k, then 2^k < q(k), so Sum_{k>=0} 1/q(k) < Sum_{k>=0} 1/2^k = 2; hence, the sum of the reciprocals of these primes q(k) form a convergent series.
%D A338475 J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 615 pp. 82 and 279, Ellipses, Paris, 2004. Warning : gives Sum_{k>=1} 1/A104080(k) = 0.7404...
%F A338475 Equals Sum_{k>=0} 1/A014210(k).
%e A338475 1.2404071466559606289464180214057283392313810734691...
%p A338475 evalf(sum(1/nextprime(2^k), k=0..infinity),90);
%t A338475 ndigits = 90; RealDigits[Sum[1/NextPrime[2^k], {k, 0, ndigits/Log10[2] + 1}], 10, ndigits][[1]] (* _Amiram Eldar_, Oct 29 2020 *)
%o A338475 (PARI) suminf(k=0, 1/nextprime(2^k+1)) \\ _Michel Marcus_, Oct 29 2020
%Y A338475 Cf. A014210, A104080, A203074.
%K A338475 nonn,cons
%O A338475 1,2
%A A338475 _Bernard Schott_, Oct 29 2020