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

%I A306591 #15 Feb 19 2023 12:53:01
%S A306591 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,
%T A306591 51,104,108,55,57,128,132,69,140,75,152,79,164,168,87,180,91,192,97,
%U A306591 99,200,212,224,228,115,117,240,121,252,129,264,135,272,139,141,284,147,308,312,157
%N A306591 a(n) is the denominator of 1/2 - 1/(prime(n)+1), where prime(n) is the n-th prime.
%H A306591 Nitya Mani and Simon Rubinstein-Salzedo, <a href="https://arxiv.org/abs/1902.09048">Diophantine Tuples over Zp</a>, arXiv:1902.09048 [math.NT], 2019. See Lemma 3.3. p. 4.
%t A306591 1/2-1/(#+1)&/@Prime[Range[70]]//Denominator (* _Harvey P. Dale_, Feb 19 2023 *)
%o A306591 (PARI) a(n) = denominator(1/2 - 1/(prime(n)+1));
%o A306591 (Python)
%o A306591 from sympy import prime
%o A306591 from fractions import Fraction
%o A306591 def a(n): return (Fraction(1, 2) - Fraction(1, (prime(n)+1))).denominator
%o A306591 print([a(n) for n in range(1, 66)]) # _Michael S. Branicky_, Jun 04 2021
%Y A306591 Cf. A236965 (numerators).
%Y A306591 Cf. A145979 (denominator of 1/2 - 1/(n+1)).
%K A306591 nonn,frac
%O A306591 1,1
%A A306591 _Michel Marcus_, Feb 26 2019