A013676 Decimal expansion of zeta(18).

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

Offset

1,7

References

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.

Links

Table of n, a(n) for n=1..99.

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Formula

zeta(18) = Sum_{n >= 1} (A010052(n)/n^9) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^9 ). - Mikael Aaltonen, Mar 06 2015

zeta(18) = 43867*Pi^18/38979295480125 = A046988(9)*Pi^18/A002432(9). - Alonso del Arte, Feb 12 2016

zeta(18) = Product_{k>=1} 1/(1 - 1/prime(k)^18). - Vaclav Kotesovec, May 02 2020

Example

1.0000038172932649998398564616446219397...

Mathematica

RealDigits[Zeta[18], 10, 100][[1]] (* Alonso del Arte, Feb 07 2016 *)

Prog

(PARI) zeta(18) \\ Michel Marcus, Feb 12 2016

Crossrefs

Sequence in context: A219995 A021266 A054399 * A199270 A131563 A016622

Adjacent sequences: A013673 A013674 A013675 * A013677 A013678 A013679

Keyword

cons,nonn

Author

N. J. A. Sloane

Status

approved