A123704 -id:A123704 - cp's OEIS frontend

A123705 Primes of the form (5^p-3^p)/2, where prime p = Prime[A123704[n]] = A121877[n].

609554401, 9536162033329, 5960417405949649, 2328306127701998147089, 355271367866755685756083382145169, 29387358770557187699218413428591111182510208390715375894150039546014062887655539136439569

Offset: 1

Alexander Adamchuk, Oct 08 2006

nonn

Corresponding primes p are listed in A121877[n] = Prime[A123704[n]] = {13, 19, 23, 31, 47, 127, 223, 281, 2083, ...} Numbers n such that (5^n-3^n)/2 is a prime. Numbers n such that (5^p-3^p)/2 is prime, where p = Prime[n], are listed in A123704[n] = {6, 8, 9, 11, 15, 31, 48, 60, 314, ...}.

Cf. A123704, A121877.

Select[(5^#-3^#)/2&/@Prime[Range[50]],PrimeQ] (* Harvey P. Dale, Mar 30 2012 *)

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

Original entry on oeis.org

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

Offset: 1

Alexander Adamchuk, Aug 31 2006, Oct 08 2006

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

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.

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

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

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

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

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

cp's OEIS Frontend

A123705 Primes of the form (5^p-3^p)/2, where prime p = Prime[A123704[n]] = A121877[n].

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

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