

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
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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

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]] (* JeanFrançois 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



