A283653 Numbers k such that 3^k + (-2)^k is prime.

0, 2, 3, 4, 5, 17, 29, 31, 53, 59, 101, 277, 647, 1061, 2381, 2833, 3613, 3853, 3929, 5297, 7417, 90217, 122219, 173191, 256199, 336353, 485977, 591827, 1059503

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 12 2017

Keywords

• nonn
• more

Comments

Numbers j such that both 3^j + (-2)^j and 3^j + (-4)^j are primes: 0, 3, 4, 17, 59, ...

See Michael Somos comment in A082101.

Probably this is just A057468 with 0,2,4 added, because we already know that if another even number belong to this sequence it must be greater than log_3(10^16000000) = about 3.3*10^7. This is because 3^n+2^n can be a prime with n>0 only if n is a power of 2. - Giovanni Resta, Mar 12 2017

Examples

			4 is in this sequence because 3^4 + (-2)^4 = 97 is prime.
		

Crossrefs

Cf. A174326. Subsequence of A087451. Supersequence of A057468.

Cf. A082101.

Programs

Magma

[n: n in [0..1000] | IsPrime(3^n+(-2)^n)];

Mathematica

Select[Range[0, 10000], PrimeQ[3^# + (-2)^#] &] (* G. C. Greubel, Jul 29 2018 *)

PARI

is(n)=isprime(3^n+(-2)^n) \\ Charles R Greathouse IV, Mar 16 2017