A307379 Decimal expansion of Sum_{n >= 1} 2/(k(n)*(k(n) + 1)), with k = A018252 (nonprime numbers).

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

Offset

1,2

Comments

We know that Sum_{n >= 1} 2/(n^2 + n) = 2 and Sum_{n >= 1} 2/(p(n)*(p(n) + 1)) = 2*A179119, where p = A000040. Therefore, the present decimal expansion 1/1 + 1/10 + 1/21 + 1/36 + ... = 2*(1 - A179119).

Links

Table of n, a(n) for n=1..87.

Formula

Equals 2*(1 - A179119) = 2*(1 - Sum_{n>=1} 1/(A000040(n)*A008864(n))).

Example

1.3395401474715935179... = 2 - (1/3 + 1/(3*2) + 1/(5*3) + 1/(7*4) + 1/(11*6)) + ...) = 2*(1 - A179119).

Mathematica

digits = 87;
S = 2 - 2 NSum[(-1)^n PrimeZetaP[n], {n, 2, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits+5];
RealDigits[S, 10, digits][[1]] (* Jean-François Alcover, Jun 20 2019 *) [From A179119]

Prog

(PARI) 2*(1 - sumeulerrat(1/(p*(p+1)))) \\ Amiram Eldar, Mar 18 2021

Crossrefs

Cf. A000040, A008864, A018252, A179119.

Sequence in context: A088032 A348397 A066572 * A276147 A300782 A104195

Adjacent sequences: A307376 A307377 A307378 * A307380 A307381 A307382

Keyword

cons,easy,nonn

Author

Marco Ripà, Apr 06 2019

Extensions

Edited by Wolfdieter Lang, Jul 10 2019

Status

approved