cp's OEIS Frontend

A098882 Decimal expansion of the Sum_{n>0} (A000040(n+1)-A000040(n))/(2^n), where A000040(k) gives the k-th prime number.

%I A098882 #15 Feb 16 2025 08:32:54
%S A098882 1,6,7,4,6,4,3,9,6,6,0,1,1,3,2,8,7,7,8,9,9,5,6,7,6,3,0,9,0,8,4,0,2,9,
%T A098882 4,1,1,6,7,7,7,9,7,5,8,8,7,7,9,4,3,7,3,2,8,3,1,2,2,0,5,2,2,0,1,7,6,3,
%U A098882 7,9,8,6,7,0,4,4,8,2,8,3,6,0,4,1,7,4,5,4,7,6,4,5,7,8,8,0,1,9,0,1,1,3,7,5,2
%N A098882 Decimal expansion of the Sum_{n>0} (A000040(n+1)-A000040(n))/(2^n), where A000040(k) gives the k-th prime number.
%H A098882 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeNumber.html">Prime Number</a>.
%F A098882 Equals A098990 - 2. - _Amiram Eldar_, Nov 17 2020
%e A098882 1.6746439660113287789956763090840294116777975887794373283122052201763...
%p A098882 g:=N->sum((ithprime(n+1)-ithprime(n))/2^n,n=1..N); evalf[106](g(5000)); evalf[106](g(10000));
%o A098882 (PARI) suminf(k=1, (prime(k+1)-prime(k))/2^k) \\ _Michel Marcus_, Jan 13 2016
%Y A098882 Cf. A000040, A098990.
%K A098882 cons,nonn
%O A098882 1,2
%A A098882 Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 03 2004