

A334993


Numbers k such that 2*3^k + 1 is prime and divides Phi(3^m, 2).


0



1, 5, 9, 17, 57, 65, 897, 4217, 6225, 152529, 3648969, 5570081
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OFFSET

1,2


COMMENTS

A subset of odd values from A003306.
If p = 2*3^k + 1 is prime then p divides 2^(3^k) + (1)^k, due to Euler's criterion.
Only odd terms of sequence A003306 can divide the cyclotomic expression Phi(3^m, 2); none of the even terms of sequence A003306 can divide 2^3^k1 and therefore cannot divide Phi(3^m, 2).


LINKS

Table of n, a(n) for n=1..12.
C. Caldwell's Prime Page for Divides Phi category.


PROG

(PARI) dp(n)=Mod(2, 2*3^n+1)^3^n==1;
forstep(n=1, 6225, 2, if(dp(n), print1(n, ", ")))


CROSSREFS

Cf. A003306.
Sequence in context: A336139 A295627 A300128 * A262484 A228956 A233584
Adjacent sequences: A334990 A334991 A334992 * A334994 A334995 A334996


KEYWORD

nonn,hard,more


AUTHOR

Serge Batalov, May 18 2020


STATUS

approved



