A306591 a(n) is the denominator of 1/2 - 1/(prime(n)+1), where prime(n) is the n-th prime.

6, 4, 3, 8, 12, 7, 9, 20, 24, 15, 32, 19, 21, 44, 48, 27, 60, 31, 68, 72, 37, 80, 84, 45, 49, 51, 104, 108, 55, 57, 128, 132, 69, 140, 75, 152, 79, 164, 168, 87, 180, 91, 192, 97, 99, 200, 212, 224, 228, 115, 117, 240, 121, 252, 129, 264, 135, 272, 139, 141, 284, 147, 308, 312, 157

Offset: 1

Author

Michel Marcus, Feb 26 2019

Keywords

• nonn
• frac

Links

• Nitya Mani and Simon Rubinstein-Salzedo, Diophantine Tuples over Zp, arXiv:1902.09048 [math.NT], 2019. See Lemma 3.3. p. 4.

Crossrefs

Cf. A236965 (numerators).

Cf. A145979 (denominator of 1/2 - 1/(n+1)).

Programs

Mathematica

1/2-1/(#+1)&/@Prime[Range[70]]//Denominator (* Harvey P. Dale, Feb 19 2023 *)

PARI

a(n) = denominator(1/2 - 1/(prime(n)+1));

Python

from sympy import prime
from fractions import Fraction
def a(n): return (Fraction(1, 2) - Fraction(1, (prime(n)+1))).denominator
print([a(n) for n in range(1, 66)]) # Michael S. Branicky, Jun 04 2021