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

Author

Serge Batalov, May 18 2020

Keywords

• nonn
• hard
• more

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

• C. Caldwell's Prime Page for Divides Phi category.

Crossrefs

Cf. A003306.

Programs

PARI

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