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A307379 Decimal expansion of Sum_{n >= 1} 2/(k(n)*(k(n) + 1)), with k = A018252 (nonprime numbers). 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified April 1 19:13 EDT 2023. Contains 361695 sequences. (Running on oeis4.)