A079081 Numerator of (prime(n)+1)*(prime(n+1)+1)/(4*(prime(n)*prime(n+1)+1)).

3, 3, 1, 4, 7, 21, 5, 20, 45, 4, 76, 133, 11, 88, 162, 405, 31, 527, 204, 37, 185, 280, 945, 735, 833, 13, 468, 55, 1045, 76, 704, 2277, 35, 875, 19, 1501, 3239, 1148, 1827, 3915, 91, 728, 97, 3201, 25, 1060, 848, 2128, 115, 4485, 1755, 121, 2541, 8127, 4257, 4455

Offset: 1

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

• nonn
• frac

Links

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

Crossrefs

Denominator = A079082.

Cf. A023523, A079079, A079080.

Programs

Haskell

a079081 n = a079081_list !! (n-1)
a079081_list = zipWith div a079079_list a079080_list
-- Reinhard Zumkeller, Oct 09 2012

Mathematica

a[n_] := Module[{p = Prime[n], q}, q = NextPrime[p]; Numerator[(p+1) * (q+1) / (4 * (p*q + 1))]]; Array[a, 100] (* Amiram Eldar, Apr 06 2025 *)

PARI

a(n) = my(p = prime(n), q = nextprime(p+1)); numerator((p+1) * (q+1) / (4 * (p*q + 1))); \\ Amiram Eldar, Apr 06 2025

Formula

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

a(n) = A079079(n)/A079080(n).