A013675 - OEIS

A013675

Decimal expansion of zeta(17).

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

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OFFSET

1,7

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, p. 811.

FORMULA

From Peter Bala, Dec 04 2013: (Start)

Definition: zeta(17) = sum {n >= 1} 1/n^17.

zeta(17) = 2^17/(2^17 - 1)*( sum {n even} n^11*p(n)*p(1/n)/(n^2 - 1)^18 ), where p(n) = n^8 + 36*n^6 + 126*n^4 + 84*n^2 + 9. Cf. A013663, A013667 and A013671.

(End)

zeta(17) = Sum_{n >= 1} (A010052(n)/n^(17/2)) = Sum_{n >= 1} ( (floor(sqrt(n)) - floor(sqrt(n-1)))/n^(17/2) ). - Mikael Aaltonen, Feb 23 2015

zeta(17) = Product_{k>=1} 1/(1 - 1/prime(k)^17). - Vaclav Kotesovec, May 02 2020

EXAMPLE

1.0000076371976378997622736002935630292130882490902626790953798439729356...

MATHEMATICA

RealDigits[Zeta[17], 10, 75][[1]] (* Vincenzo Librandi, Feb 24 2015 *)

PROG

(PARI) zeta(17) \\ Charles R Greathouse IV, Dec 04 2013

CROSSREFS

Cf. A013663, A013667, A013669, A013671, A013675, A013677, A010057.

Sequence in context: A371934 A199437 A021571 * A198878 A332982 A335996

Adjacent sequences: A013672 A013673 A013674 * A013676 A013677 A013678

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane

STATUS

approved