A137332 Primes which are equal to the order of 2 modulo a prime q, sorted with respect to the value of q.

2, 3, 11, 5, 23, 11, 7, 83, 37, 29, 131, 179, 191, 43, 73, 239, 251, 359, 419, 431, 443, 491, 29, 659, 683, 233, 179, 719, 743, 911, 239, 1019, 1031, 29, 1103, 47, 397, 1223, 79, 461, 1439, 1451, 1499, 1511, 1559, 1583, 557, 113, 431, 577, 601, 1811, 1931

Offset: 1

Author

Joerg Arndt, Apr 07 2008

Keywords

• nonn

Comments

This is a multipermutation of the primes A000040 with every prime p appearing exactly A001221(2^p-1) times. - Max Alekseyev, May 01 2008

Examples

			The k-th term of the sequence is ord(2 mod A122094(k)).
For example, 223 is the 9th term of A122094 and ord(2 mod 223)=37, so 37 is the 9th term of this sequence.
11 is both the third term because ord(2 mod 23) == 11 and the sixth term because ord(2 mod 89) == 11.
Note both 23 and 89 divide 2^11-1; the third and sixth terms of A122094 are 23 and 89.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..106 from Joerg Arndt)

Crossrefs

Cf. A002326, A122094.

Programs

Mathematica

Select[MultiplicativeOrder[2, #] & /@ Select[Range[3, 4000, 2], PrimeQ], PrimeQ] (* Amiram Eldar, Apr 04 2020 *)

PARI

forprime (p=3, 10^4, r = znorder( Mod(2,p) ); if ( isprime(r), print1(r, ", "); ); );

Formula

a(n) = A007733(A122094(n)) = A002326((A122094(n)-1)/2). - Max Alekseyev, May 01 2008

Extensions

Definition revised by Max Alekseyev, May 01 2008