A127438 -id:A127438 - cp's OEIS frontend

A191609 Primes modulo which the multiplicative orders of 2 and 3 are equal.

5, 19, 23, 29, 47, 53, 71, 97, 101, 139, 149, 163, 167, 173, 191, 197, 211, 239, 263, 269, 293, 311, 317, 359, 379, 383, 389, 409, 431, 461, 479, 499, 503, 509, 557, 599, 643, 647, 653, 677, 701, 719, 743, 773, 797, 821, 839, 859, 863, 887, 907, 941, 983

Offset: 1

Max Alekseyev, Jun 08 2011

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A123988, A127437, A127438.

select(p -> isprime(p) and numtheory:-order(2,p) = numtheory:-order(3,p), [seq(i,i=5..10000,2)]); # Robert Israel, Jan 24 2024

okQ[p_] := MultiplicativeOrder[2, p] == MultiplicativeOrder[3, p];
Select[Prime[Range[1000]], okQ] (* Jean-François Alcover, Nov 23 2024 *)

forprime(p=5,10^3, if( znorder(Mod(2,p))==znorder(Mod(3,p)), print1(p,", ");) )

A127437 Duplicate of A001915.

Original entry on oeis.org

2, 5, 11, 13, 19, 23, 29, 37, 47, 53, 59, 61, 67, 71, 83, 97, 101, 107, 131, 139, 149, 163, 167, 173, 179, 181, 191, 193, 197, 211, 227, 239, 263, 269, 293, 307, 311, 313, 317, 347, 349, 359, 373, 379, 383, 389, 409, 419, 421, 431, 443, 461, 467, 479, 491, 499, 503, 509, 523, 541, 547, 557, 563, 577

Offset: 1

Max Alekseyev, Jan 14 2007

dead

Potential prime divisors of solutions to 2^m == 3 (mod m) (see A050259).

Minimal nonnegative solutions to 2^x == 3 (mod a(n)) are given in A127438.

Cf. A050259, A123988 (complement in the primes).

forprime(p=5,1000, g=znprimroot(p); u=znlog(Mod(2,p),g); v=znlog(Mod(3,p),g); if( v%u==0, print1(p,", "); ))

Corrected by Max Alekseyev, Jun 08 2011

Corrected by Arkadiusz Wesolowski, Jan 12 2021

cp's OEIS Frontend

A191609 Primes modulo which the multiplicative orders of 2 and 3 are equal.

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