A389877 Number of digits in numerators of zeta(2*n)/Pi^(2*n).

1, 1, 1, 1, 1, 1, 3, 1, 4, 5, 6, 6, 9, 7, 10, 13, 13, 12, 20, 15, 21, 22, 22, 24, 28, 26, 30, 33, 33, 35, 43, 37, 42, 45, 42, 47, 55, 49, 52, 57, 61, 59, 67, 62, 69, 72, 72, 72, 81, 76, 84, 83, 85, 88, 98, 95, 99, 97, 101, 101, 114, 106, 108, 117, 117, 119, 125

Offset

0,7

Links

Jwalin Bhatt, Table of n, a(n) for n = 0..5000

Formula

a(n) = A055642(A046988(n)).

Mathematica

a[n_]:=IntegerLength[Numerator[Zeta[2n]/Pi^(2n)]]; Array[a, 67, 0] (* Stefano Spezia, Oct 20 2025 *)

Prog

(Python)
from sympy import bernoulli, factorial
def pi_frac(n):
   s = 1 if n//2%2 else -1
   return s * (2**(n-1)) * bernoulli(n) / factorial(n)
A389877 = [1] + [len(str(pi_frac(i).numerator)) for i in range(2, 101, 2)]

Crossrefs

Cf. A046988, A055642, A389876.

Sequence in context: A302917 A069203 A046070 * A068399 A225407 A353292

Adjacent sequences: A389874 A389875 A389876 * A389878 A389879 A389880

Keyword

nonn,base

Author

Jwalin Bhatt, Oct 18 2025

Status

approved