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

1,2

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

Links

Table of n, a(n) for n=1..29.

Example

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

Mathematica

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

Prog

(Magma) [n: n in [0..1000] | IsPrime(3^n+(-2)^n)];
(PARI) is(n)=isprime(3^n+(-2)^n) \\ Charles R Greathouse IV, Mar 16 2017

Crossrefs

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

Cf. A082101.

Sequence in context: A117885 A030574 A325652 * A162657 A333046 A305794

Adjacent sequences: A283650 A283651 A283652 * A283654 A283655 A283656

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Mar 12 2017

Status

approved