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

1,2

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Prime Number.

Formula

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

Example

1.6746439660113287789956763090840294116777975887794373283122052201763...

Maple

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

Prog

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

Crossrefs

Cf. A000040, A098990.

Sequence in context: A004447 A258989 A005351 * A254374 A019616 A274209

Adjacent sequences: A098879 A098880 A098881 * A098883 A098884 A098885

Keyword

cons,nonn

Author

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

Status

approved