A253358 Decimal expansion of Sum_{n>=1} prime(n)/n^3.

3, 3, 3, 9, 5, 3

Offset

1,1

Comments

Since prime(n) ~ n*log(n), Sum_{n>=1} prime(n)/n^j converges for j > 2.

Links

Table of n, a(n) for n=1..6.

Example

3.339530...
The first few partial sums are:
up to prime(n)=2, 2/1^3 = 2.0;
up to prime(n)=3, 2 + 3/2^3 = 2.375;
up to prime(n)=5, 2 + 3/2^3 + 5/3^3 = 2.56018;
The partial sum for n <= 100000 is 3.3393903401...
The partial sum for n <= 1000000 is 3.33951457002...
The partial sum for n <= 5000000 is 3.3395274693...
The partial sum for n <= 10000000 is 3.339529222...
The partial sum for prime(n) <= 999999937 is 3.33953071535199...

Crossrefs

Cf. A253357 (sum over prime(n)/n^4).

Sequence in context: A161332 A217547 A285583 * A256566 A132171 A304682

Adjacent sequences: A253355 A253356 A253357 * A253359 A253360 A253361

Keyword

nonn,cons,more

Author

Olivier Izad, Dec 30 2014

Status

approved