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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 FORMULA 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] CROSSREFS Cf. A000040, A008864, A018252, A179119. Sequence in context: A113213 A088032 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 December 9 15:04 EST 2019. Contains 329877 sequences. (Running on oeis4.)