A013678 - OEIS

A013678

Decimal expansion of zeta(20).

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

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OFFSET

1,8

REFERENCES

M. Abramowitz and I. 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.

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

FORMULA

zeta(20) = Sum_{n >= 1} (A010052(n)/n^10) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^10 ). - Mikael Aaltonen, Mar 06 2015

zeta(20) = 174611 * Pi^20 / 1531329465290625. - Vaclav Kotesovec, May 15 2019

zeta(20) = Product_{k>=1} 1/(1 - 1/prime(k)^20). - Vaclav Kotesovec, May 02 2020

EXAMPLE

1.00000095396203387279611315203868344934594379418741059575005648985113...

MATHEMATICA

RealDigits[Zeta[20], 10, 120][[1]] (* Harvey P. Dale, Jun 21 2015 *)

CROSSREFS

Sequence in context: A057888 A182125 A010542 * A336334 A139604 A104139

Adjacent sequences: A013675 A013676 A013677 * A013679 A013680 A013681

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane

STATUS

approved