A098882 - OEIS

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

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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));