

A253634


Decimal expansion of Sum_{n>=1} 1/A033286(n)^2.


0



2, 8, 4, 1, 7, 0, 7, 0, 5, 4, 7, 0, 8, 6, 8, 2, 5, 0, 1, 7, 7, 1, 4
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OFFSET

0,1


COMMENTS

The convergence is very slow, need to use the first 100000000 primes to obtain the correct value of the coefficient of 10^(23).
The constant is in the interval [0.28417070547086825017714, 0.28417070547086825017743]; these safe limits are computed by accumulating in parallel the partial sum of the lower estimate 1/n^4 = Zeta(4).  R. J. Mathar, Feb 06 2015
The next digits after ...17714 appear to be 3618.  Jon E. Schoenfield, Jan 05 2019


LINKS

Table of n, a(n) for n=0..22.


EXAMPLE

0.284170705470...


PROG

(PFGW & SCRIPT)
SCRIPT
DIM i, 0
DIM j, 0
DIM n
DIM m
DIMS t
OPENFILEOUT myf, a(n).txt
OPENFILEIN maf, pre.txt
LABEL loop1
SET i, i+1
IF i>10000000 THEN END
GETNEXT n, maf
SET j, j+10^10000/((i*n)^2)
IF i%1000000==0 THEN SET m, j/10^9970
IF i%1000000==0 THEN WRITE myf, m
GOTO loop1


CROSSREFS

Cf. A033286 (n*prime(n)), A124012.
Sequence in context: A264818 A264709 A200004 * A152626 A093823 A088154
Adjacent sequences: A253631 A253632 A253633 * A253635 A253636 A253637


KEYWORD

nonn,cons,more


AUTHOR

Pierre CAMI, Jan 07 2015


STATUS

approved



