A123988 Primes p such that 2^x == 3 (mod p) has no solutions.

3, 7, 17, 31, 41, 43, 73, 79, 89, 103, 109, 113, 127, 137, 151, 157, 199, 223, 229, 233, 241, 251, 257, 271, 277, 281, 283, 331, 337, 353, 367, 397, 401, 433, 439, 449, 457, 463, 487, 521, 569, 571, 593, 601, 607, 617, 631, 641, 673, 683, 691, 727, 733, 739, 751, 761, 809, 811, 823, 857, 881, 911

Offset

1,1

Comments

Such primes cannot divide solutions to 2^m == 3 (mod m) (see A050259).

Links

Table of n, a(n) for n=1..62.

J. K. Crump, Number Theory Web.

Prog

(Magma) lst:=[3]; for p in [5..911 by 2] do if IsPrime(p) then t:=0; e:=Ceiling(Log(2, p+1)); for x in [e..p-2] do if 2^x mod p eq 3 then t:=1; break; end if; end for; if t eq 0 then Append(~lst, p); end if; end if; end for; lst; // Arkadiusz Wesolowski, Jan 12 2021

Crossrefs

Cf. A050259, A001915 (complement in the primes).

Sequence in context: A079779 A083991 A228567 * A006628 A068682 A292446

Adjacent sequences: A123985 A123986 A123987 * A123989 A123990 A123991

Keyword

nonn

Author

Artur Jasinski, Nov 23 2006

Extensions

Edited by Max Alekseyev, Jan 14 2007

Corrected by Max Alekseyev, Jun 08 2011

Corrected by Arkadiusz Wesolowski, Jan 12 2021

Status

approved