# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a098882 Showing 1-1 of 1 %I A098882 #14 Nov 17 2020 05:39:37 %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, Prime Number. %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE