A123704 Numbers k such that (5^p - 3^p)/2 is prime, where p = prime(k).

6, 8, 9, 11, 15, 31, 48, 60, 314, 701, 940, 942, 2164, 2981, 3810, 6971, 12068, 13641, 16502, 68800

Offset: 1

Author

Alexander Adamchuk, Oct 08 2006

Keywords

• nonn
• more

Comments

The corresponding primes p = prime(a(n)) are listed in A121877.

The corresponding primes of the form (5^p - 3^p)/2 are listed in A123705.

a(13) is greater than 1000. - Farideh Firoozbakht, Oct 11 2006

Crossrefs

Cf. A005059, A121877, A123705.

Programs

Mathematica

Do[If[PrimeQ[(5^Prime[n] - 3^Prime[n])/2], Print[n]], {n, 1000}] (* Robert G. Wilson v, Jan 12 2007 *)
PrimePi[#]&/@Select[Prime[Range[1000]],PrimeQ[(5^#-3^#)/2]&] (* Harvey P. Dale, Sep 23 2018 *)

Formula

a(n) = primepi(A121877(n)).

Extensions

More terms from Farideh Firoozbakht, Oct 11 2006

a(13)-a(16) computed from A121877 by Jinyuan Wang, Mar 23 2020

a(17)-a(19) from Kellen Shenton, May 18 2022

a(20) from Amiram Eldar, Sep 06 2024