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A367649
Primes p such that the multiplicative order of 3 modulo p is 2 times a power of 3.
2
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.
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
KEYWORD
nonn,hard,more
AUTHOR
Jianing Song, Nov 25 2023
EXTENSIONS
a(28)-a(31) from Chai Wah Wu, Nov 26 2023
STATUS
approved