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A342974
Primes p such that the order of 2 modulo p is not divisible by the largest odd divisor of p - 1.
0
31, 43, 109, 127, 151, 157, 223, 229, 241, 251, 277, 283, 307, 331, 397, 431, 433, 439, 457, 499, 571, 601, 631, 641, 643, 673, 683, 691, 727, 733, 739, 811, 911, 919, 953, 971, 997, 1013, 1021, 1051, 1069, 1093, 1103, 1163, 1181, 1321, 1327, 1399, 1423, 1429
OFFSET
1,1
COMMENTS
Every prime factor of a composite Fermat number belongs to this sequence.
If a prime of the form 3*2^k + 1 belongs to this sequence, then k is in A204620 (see Golomb).
Primes p such that A014664(primepi(p)) is not divisible by A057023(primepi(p)). - Michel Marcus, Apr 26 2021
LINKS
Solomon W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.
MATHEMATICA
Select[Prime@Range@300, Mod[MultiplicativeOrder[2, #], Max@Select[Divisors[#-1], OddQ]]!=0&] (* Giorgos Kalogeropoulos, Apr 02 2021 *)
PROG
(PARI) forprime(p=3, 1429, if(Mod(znorder(Mod(2, p)), (p-1)>>valuation(p-1, 2)), print1(p, ", ")));
KEYWORD
nonn
AUTHOR
STATUS
approved