A367649 Primes p such that the multiplicative order of 3 modulo p is 2 times a power of 3.

7, 19, 37, 163, 487, 1297, 1459, 2917, 19441, 19927, 39367, 59779, 131221, 208657, 224209, 572023, 2051893, 5062663, 8503057, 19131877, 44457337, 86093443, 113863969, 133923133, 258280327, 565571323, 600830137, 859270843, 1319934691, 4161183031, 5366491219

Offset

1,1

Comments

Odd prime factors of numbers of the form 3^3^i + 1: for odd primes p, p divides 3^3^i + 1 if and only if the multiplicative order of 3 modulo p is 2 times a power of 3 not exceeding 3^i.

Links

Table of n, a(n) for n=1..31.

Example

37 is a term since the multiplicative order of 3 modulo 37 is 18 = 2*3^2, which means that 37 is a factor of 3^3^2 + 1.
163 is a term since the multiplicative order of 3 modulo 163 is 162 = 2*3^4, which means that 163 is a factor of 3^3^4 + 1.

Prog

(PARI) isA367649(n) = my(d); isprime(n) && (n!=3) && ((d=znorder(Mod(3, n)))%2==0) && isprimepower(3*d/2)

Crossrefs

Subsequence of A367266.

Cf. A367648 (ord(3,p) being a power of 3, prime factors of numbers of the form 3^3^i - 1), 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)).

Sequence in context: A155227 A155319 A155318 * A155280 A155365 A155364

Adjacent sequences: A367646 A367647 A367648 * A367650 A367651 A367652

Keyword

nonn,hard,more

Author

Jianing Song, Nov 25 2023

Extensions

a(28)-a(31) from Chai Wah Wu, Nov 26 2023

Status

approved