

A283653


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


4



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
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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: A240906 A117885 A030574 * A162657 A305794 A317944
Adjacent sequences: A283650 A283651 A283652 * A283654 A283655 A283656


KEYWORD

nonn,more


AUTHOR

JuriStepan Gerasimov, Mar 12 2017


STATUS

approved



