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

7, 8, 3, 13, 24, 74, 18, 73, 167, 15, 287, 506, 42, 337, 623, 1564, 120, 2044, 793, 144, 721, 1093, 3694, 2878, 3266, 51, 1837, 216, 4106, 299, 2773, 8974, 138, 3452, 75, 5927, 12796, 4537, 7223, 15484, 360, 2881, 384, 12674, 99, 4199, 3361, 8437, 456

Offset: 1

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

• nonn
• frac

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Numerator = A079081.

Cf. A023523, A079079, A079080.

Programs

Haskell

a079082 n = a079082_list !! (n-1)
a079082_list = zipWith div (tail a023523_list) a079080_list
-- Reinhard Zumkeller, Oct 09 2012

Mathematica

((#[[1]]+1)(#[[2]]+1))/(4(Times@@#+1))&/@Partition[Prime[Range[50]],2,1]//Denominator (* Harvey P. Dale, Jan 01 2018 *)

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

Formula

a(n) = denominator(A079079(n)/A023523(n+1)).

a(n) = A023523(n+1)/A079080(n).