A013677 Decimal expansion of zeta(19).

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

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(19) = Sum_{n >= 1} (A010052(n)/n^(19/2)) = Sum_{n >= 1} ( (floor(sqrt(n)) - floor(sqrt(n-1)))/n^(19/2) ). - Mikael Aaltonen, Feb 23 2015

zeta(19) = Product_{k>=1} 1/(1 - 1/prime(k)^19). - Vaclav Kotesovec, May 02 2020

Example

1.0000019082127165539389256569577951013532585711448386302359330467618239...

Mathematica

RealDigits[Zeta[19], 10, 75][[1]] (* Vincenzo Librandi, Feb 24 2015 *)

Crossrefs

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

Sequence in context: A242711 A178229 A021995 * A021528 A210973 A154185

Adjacent sequences: A013674 A013675 A013676 * A013678 A013679 A013680

Keyword

cons,nonn

Author

N. J. A. Sloane

Status

approved