A282469 Decimal expansion of sum of reciprocals of fourth powers of the nonprime numbers.

1, 0, 0, 5, 3, 3, 0, 0, 9, 3, 9, 4, 6, 8, 9, 1, 3, 4, 6, 5, 7, 3, 3, 8, 4, 4, 0, 0, 6, 0, 8, 0, 1, 0, 0, 3, 2, 6, 1, 2, 7, 0, 9, 8, 9, 2, 2, 0, 3, 8, 8, 3, 7, 1, 7, 4, 1, 8, 0, 3, 8, 2, 0, 6, 5, 8, 4, 9, 0, 4, 0, 4, 5, 6, 9, 9, 4, 0, 4, 6, 4, 0, 0, 4, 6, 5, 7, 6, 5, 2, 9, 1, 5, 6, 3, 0, 3, 6, 2, 7, 6, 9, 0, 9, 6

Offset

1,4

Links

Table of n, a(n) for n=1..105.

Formula

Sum_{n>=1} 1/A018252(n)^4.

Sum_{n>=1} 1/n^4 - Sum_{n>=1} 1/A000040(n)^4.

Equals zeta(4) - primezeta(4) = A013662 - A085964.

Example

Equals 1/1^4 + 1/4^4 + 1/6^4 + 1/8^4 + 1/9^4... =
1.0053300939468913465733844006080...

Mathematica

RealDigits[Zeta[4] - PrimeZetaP[4], 10, 105][[1]]

Prog

(PARI) zeta(4) - sumeulerrat(1/p, 4) \\ Amiram Eldar, Mar 19 2021

Crossrefs

Cf. A018252, A013662, A085964.

Sequence in context: A262225 A330092 A064812 * A216998 A346469 A068118

Adjacent sequences: A282466 A282467 A282468 * A282470 A282471 A282472

Keyword

nonn,cons

Author

Terry D. Grant, Apr 14 2017

Status

approved