A280004 -id:A280004 - cp's OEIS frontend

A280003 Numbers k such that 7*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m.

Original entry on oeis.org

14, 120, 290, 320, 95330, 2167800

Offset: 1

Arkadiusz Wesolowski, Feb 21 2017

18233956 belongs to this sequence, but its position is currently unknown. - Jeppe Stig Nielsen, Oct 05 2020

Proth Search Page, Prime factors of Fermat numbers
Eric Weisstein's World of Mathematics, Fermat Number

Subsequence of A032353.

Cf. A000215, A050527, A057778, A201364, A204620, A226366, A280004.

IsInteger := func; [n: n in [1..320] | IsPrime(k) and IsInteger(Log(2, Modorder(2, k))) where k is 7*2^n+1];

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

Original entry on oeis.org

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

Arkadiusz Wesolowski, Apr 01 2021

nonn

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

Solomon W. Golomb, Properties of the sequence 3.2^n+1, Math. Comp., 30 (1976), 657-663.

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

Select[Prime@Range@300,Mod[MultiplicativeOrder[2,#],Max@Select[Divisors[#-1],OddQ]]!=0&] (* Giorgos Kalogeropoulos, Apr 02 2021 *)

forprime(p=3, 1429, if(Mod(znorder(Mod(2, p)), (p-1)>>valuation(p-1, 2)), print1(p, ", ")));

cp's OEIS Frontend

A280003 Numbers k such that 7*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m.

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