A367648 Primes p such that the multiplicative order of 3 modulo p is a power of 3.

2, 13, 109, 433, 757, 3889, 8209, 17497, 52489, 58321, 70957, 1190701, 1705861, 2598157, 6627097, 13463173, 57395629, 23245229341, 79320757897, 1069604540569, 1631815099669, 5774114968057, 8635817966221, 23765922477217, 43781455818469, 307283335691329

Offset

1,1

Comments

Prime factors of numbers of the form 3^3^i - 1: p divides 3^3^i - 1 if and only if the multiplicative order of 3 modulo p is a power of 3 not exceeding 3^i.

Links

Table of n, a(n) for n=1..26.

Example

13 is a term since the multiplicative order of 3 modulo 13 is 3 = 3^1, which means that 13 is a factor of 3^3^1 - 1.
109 is a term since the multiplicative order of 3 modulo 109 is 27 = 3^3, which means that 109 is a factor of 3^3^3 - 1.

Prog

(PARI) isA367648(n) = isprime(n) && (n!=3) && isprimepower(3*znorder(Mod(3, n)))

Crossrefs

Subsequence of A367265.

Cf. A023394 (ord(2,p) being a power of 2, prime factors of numbers of the form 2^2^i - 1 (or of the form 2^2^i + 1)), A367649 (ord(3,p) being 2 times a power of 3, prime factors of numbers of the form 3^3^i + 1).

Sequence in context: A396418 A371581 A264621 * A245806 A192204 A176932

Adjacent sequences: A367645 A367646 A367647 * A367649 A367650 A367651

Keyword

nonn,hard

Author

Jianing Song, Nov 25 2023

Extensions

a(18)-a(19) from Michel Marcus, Nov 27 2023

a(20)-a(25) from Max Alekseyev, Jul 22 2024

a(26) from Jinyuan Wang, Jan 29 2025

Status

approved