

A258187


Numbers n such that either n^k  1 or n^k  2 is prime for some positive k, but not both.


0



3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 83, 84, 85, 87, 89, 90, 91, 93, 95, 97, 98, 99, 101
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OFFSET

1,1


COMMENTS

10 is not in the sequence because all 10^k2 are even and 10^k1 are divisible by 3 (because 10^k mod 3 = 1 as 10 mod 3 =1). 16 is not in the sequence because 16^k2 are even and because 16^k1 are divisible by 3 (because 16^k mod 3 = 1 as 16 mod 3 =1). For the same reason almost all even numbers of the form 3m+1 (A016957) are absent, the only exception being 4 where 4^11 is a prime.  R. J. Mathar, Jul 22 2015
36 is not in the sequence because 36^k1 are even and 36^k1 are divisible by 5 (because 36^k mod 5 =1 as 36 mod 5 =1). This reasoning excludes all numbers of A017341 (except 6 where 6^11 is prime) from this sequence. With the same methology we can fish for (and exclude) even numbers of the form m*p+1 for primes p>=3.  R. J. Mathar, Jul 22 2015


LINKS

Table of n, a(n) for n=1..74.


EXAMPLE

2 is not in this sequence because 2^2  1 = 3 and 2^2  2 = 2 are both prime,
3 is in this sequence because 3^1  1 = 2 (prime) and 3^1  2 = 1 (nonprime) or 3^2  1 = 5 (prime) and 3^2  2 = 4 (nonprime).


PROG

(PARI) is(n)=n>2 && if(n%2, 1, isprime(n1)) \\ Charles R Greathouse IV, Jun 03 2015


CROSSREFS

Sequence in context: A304806 A304810 A026469 * A039237 A039181 A298111
Adjacent sequences: A258184 A258185 A258186 * A258188 A258189 A258190


KEYWORD

nonn,easy


AUTHOR

JuriStepan Gerasimov, May 23 2015


STATUS

approved



