A334993 Numbers k such that 2*3^k + 1 is prime and divides Phi(3^m, 2).

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

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^k-1 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