A342974 Primes p such that the order of 2 modulo p is not divisible by the largest odd divisor of p - 1.

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

Table of n, a(n) for n=1..50.

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, ", ")));

Crossrefs

Cf. A014664, A023394, A057023, A204620, A226366, A280003, A280004.

Sequence in context: A266989 A161615 A307950 * A347035 A364186 A059898

Adjacent sequences: A342971 A342972 A342973 * A342975 A342976 A342977

Keyword

nonn

Author

Arkadiusz Wesolowski, Apr 01 2021

Status

approved