A121877 Numbers k such that (5^k - 3^k)/2 = A005059(k) is prime.

13, 19, 23, 31, 47, 127, 223, 281, 2083, 5281, 7411, 7433, 19051, 27239, 35863, 70327, 128941, 147571, 182099, 866029

Offset: 1

Author

Alexander Adamchuk, Aug 31 2006, Oct 08 2006

Keywords

• nonn
• hard
• more

Comments

All terms are primes. Their indices are listed in A123704.

Corresponding primes are listed in A123705.

If it exists, a(17) > 125000. - Robert Price, Aug 15 2011

If it exists, a(21) > 1000000. - Jon Grantham, Jul 29 2023

Links

• OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b).
• Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Crossrefs

Cf. A005058, A005059, A109347, A120612, A081186, A121824, A123704, A123705.

Programs

Mathematica

Do[f=(5^n-3^n)/2;If[PrimeQ[f],Print[{n,f}]],{n,1,300}]

PARI

forprime(p=2,1e4,if(ispseudoprime((5^p-3^p)>>1),print1(p", "))) \\ Charles R Greathouse IV, Jun 16 2011

Formula

a(n) = prime(A123704(n)).

Extensions

More terms from Farideh Firoozbakht, Oct 11 2006

a(13)-a(16) from Robert Price, Aug 15 2011

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

a(20) from Jon Grantham, Jul 29 2023