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A282469
Decimal expansion of sum of reciprocals of fourth powers of the nonprime numbers.
0
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
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
KEYWORD
nonn,cons
AUTHOR
Terry D. Grant, Apr 14 2017
STATUS
approved