A076515 Numbers k such that 1 + 3^k + 5^k is prime.

0, 12, 36, 48, 72, 120, 605376

Offset: 1

Author

Zak Seidov, Oct 17 2002

Keywords

• nonn
• more

Comments

Next term, if it exists, is greater than 35000. - Vaclav Kotesovec, Jan 26 2016

No more terms up to 75000 (previous range rechecked). All terms are multiples of 12: if k > 0 is not a multiple of 12, 1 + 3^k + 5^k is divisible by 3, 5 or 7. - Rick L. Shepherd, Aug 06 2017

Next term, if it exists, is greater than 10^6. - Jon Grantham, Jul 29 2023

Crossrefs

Cf. A008594, A074507, A268064, A268065, A268067.

Programs

Magma

[n: n in [0..1000]|IsPrime(3^n+5^n+1)] // Vincenzo Librandi, Jan 22 2011

Maple

A076515:=n->`if`(isprime(1+3^n+5^n), n, NULL): seq(A076515(n), n=0..200); # Wesley Ivan Hurt, Aug 06 2017

Mathematica

Do[ If[ PrimeQ[1 + 3^n + 5^n], Print[n]], {n, 0, 3500, 2}]
Select[Range[0,5000],PrimeQ[1+3^#+5^#]&] (* Harvey P. Dale, Mar 09 2012 *)

PARI

lista(nn) = for(n=0, nn, if(ispseudoprime(1 + 3^n + 5^n), print1(n, ", "))); \\ Altug Alkan, Jan 25 2016

Extensions

a(7) from Jon Grantham, Jul 29 2023