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A079082 Denominator of (prime(n)+1)*(prime(n+1)+1)/(4*(prime(n)*prime(n+1)+1)).

%I A079082 #18 Apr 07 2025 09:51:02
%S A079082 7,8,3,13,24,74,18,73,167,15,287,506,42,337,623,1564,120,2044,793,144,
%T A079082 721,1093,3694,2878,3266,51,1837,216,4106,299,2773,8974,138,3452,75,
%U A079082 5927,12796,4537,7223,15484,360,2881,384,12674,99,4199,3361,8437,456
%N A079082 Denominator of (prime(n)+1)*(prime(n+1)+1)/(4*(prime(n)*prime(n+1)+1)).
%H A079082 Reinhard Zumkeller, <a href="/A079082/b079082.txt">Table of n, a(n) for n = 1..10000</a>
%F A079082 a(n) = denominator(A079079(n)/A023523(n+1)).
%F A079082 a(n) = A023523(n+1)/A079080(n).
%t A079082 ((#[[1]]+1)(#[[2]]+1))/(4(Times@@#+1))&/@Partition[Prime[Range[50]],2,1]//Denominator (* _Harvey P. Dale_, Jan 01 2018 *)
%o A079082 (Haskell)
%o A079082 a079082 n = a079082_list !! (n-1)
%o A079082 a079082_list = zipWith div (tail a023523_list) a079080_list
%o A079082 -- _Reinhard Zumkeller_, Oct 09 2012
%o A079082 (PARI) a(n) = my(p = prime(n), q = nextprime(p+1)); denominator((p+1) * (q+1) / (4 * (p*q + 1))); \\ _Amiram Eldar_, Apr 06 2025
%Y A079082 Numerator = A079081.
%Y A079082 Cf. A023523, A079079, A079080.
%K A079082 nonn,frac
%O A079082 1,1
%A A079082 _Reinhard Zumkeller_, Dec 22 2002