A382598 - OEIS

A382598

Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p*(p + 1)^2).

0, 5, 8, 2, 5, 7, 7, 9, 8, 0, 9, 9, 0, 7, 2, 1, 6, 8, 7, 3, 3, 2, 2, 3, 5, 0, 2, 6, 0, 1, 5, 8, 4, 2, 8, 1, 0, 6, 2, 6, 1, 6, 5, 1, 0, 2, 8, 7, 5, 0, 7, 9, 5, 0, 0, 0, 0, 4, 4, 3, 6, 1, 5, 4, 2, 1, 9, 7, 3, 3, 3, 9, 1, 3, 9, 5, 7, 9, 7, 3, 9, 3, 5, 4, 0, 9, 8, 7, 6, 8, 1, 3, 6, 0, 1, 2, 7, 1, 5, 3, 5, 5, 2

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..102.

Index to constants which are prime zeta sums {1,3,2}.

FORMULA

Equals 11*A136141/16 - A086242/2 + A380840/4 - 5*A179119/16 + A382554/8.

Equals Sum_{k>=3} ((k-2)*(k-1)/2)*(P(2*k) + P(2*k+1)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

EXAMPLE

0.05825779809907216873322350260158428106261651028750...

PROG