A253634 Decimal expansion of Sum_{n>=1} 1/A033286(n)^2.

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

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

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