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

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, 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, 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

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 03 2004

Keywords

• cons
• nonn

Examples

			1.6746439660113287789956763090840294116777975887794373283122052201763...
		

Links

• Eric Weisstein's World of Mathematics, Prime Number.

Crossrefs

Cf. A000040, A098990.

Programs

Maple

g:=N->sum((ithprime(n+1)-ithprime(n))/2^n,n=1..N); evalf[106](g(5000)); evalf[106](g(10000));

PARI

suminf(k=1, (prime(k+1)-prime(k))/2^k) \\ Michel Marcus, Jan 13 2016

Formula

Equals A098990 - 2. - Amiram Eldar, Nov 17 2020