A268064 Integers k such that (2^k + 1) + (3^k + 1) + (5^k + 1) is prime.

1, 2, 3, 6, 10, 15, 30, 34, 35, 46, 55, 62, 83, 230, 1675, 2551, 3934, 25101, 28703, 46295, 54363, 72846

Offset

1,2

Comments

Inspired by A268067.

Integers k such that A000051(k) + A034472(k) + A034474(k) is a prime number.

Corresponding primes are 13, 41, 163, 16421, 9825701, 30531959803, 931322780507684352101, 582076625811872951801381, 2910383095704949820066203, ...

a(18) > 10000. - Tyler NeSmith, May 07 2021

Links

Table of n, a(n) for n=1..22.

Example

2 is a term because (2^2 + 1) + (3^2 + 1) + (5^2 + 1) = 41 is prime.

Mathematica

Select[Range[0, 2000], PrimeQ[(2^#+1) + (3^#+1) + (5^#+1)] &] (* Vaclav Kotesovec, Jan 26 2016 *)

Prog

(PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(3 + 2^n + 3^n + 5^n), print1(n, ", ")));

Crossrefs

Cf. A000051, A034472, A034474, A268067.

Sequence in context: A369425 A018141 A178659 * A077011 A246868 A370819

Adjacent sequences: A268061 A268062 A268063 * A268065 A268066 A268067

Keyword

nonn,hard,more

Author

Altug Alkan, Jan 25 2016

Extensions

a(18)-a(19) from Michael S. Branicky, Apr 12 2023

a(20)-a(22) from Michael S. Branicky, Sep 18 2024

Status

approved