A383463 Decimal expansion of Sum_{k>=0} 1/(16*k+1)^3.

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

Offset

1,5

Links

Jason Bard, Table of n, a(n) for n = 1..10000

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 21.

Formula

Equals -1/8192 * PolyGamma(2, 1/16).

Example

1.00024930487675326174813579820380197902155271564286...

Maple

evalf(sum(1/(16*k+1)^3, k=0..infinity), 120);  # Alois P. Heinz, Jul 26 2025

Mathematica

RealDigits[-PolyGamma[2, 1/16]/8192, 10, 100][[1]]

Prog

(PARI) zetahurwitz(3, 1/16)/16^3 \\ Amiram Eldar, Jul 28 2025

Crossrefs

Sequence in context: A229351 A229353 A133057 * A155523 A019912 A354903

Adjacent sequences: A383460 A383461 A383462 * A383464 A383465 A383466

Keyword

nonn,cons

Author

Jason Bard, Jul 24 2025

Status

approved