A379865 Number of base 10 digits of 2^(p-1)*(2^p-1) where p = prime(n).

1, 2, 3, 4, 7, 8, 10, 12, 14, 18, 19, 22, 25, 26, 28, 32, 36, 37, 41, 43, 44, 48, 50, 54, 59, 61, 62, 65, 66, 68, 77, 79, 83, 84, 90, 91, 95, 98, 101, 104, 108, 109, 115, 116, 119, 120, 127, 134, 137, 138, 140, 144, 145, 151, 155, 159, 162, 163, 167, 169, 171, 177

Offset: 1

Author

Darío Clavijo, Jan 04 2025

Keywords

• nonn
• easy
• base

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034887, A055642, A060286.

Programs

Mathematica

A379865[n_] := IntegerLength[2^(# - 1)*(2^# - 1)] & [Prime[n]];
Array[A379865, 100] (* Paolo Xausa, Jan 08 2025 *)

Python

from sympy import prime
def a(n):
  p = prime(n)
  return len(str((1 << (p-1)) * ((1 << p) - 1)))
print([a(n) for n in range(1,63)])

Formula

a(n) = A055642(A060286(n)).