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

1,1

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A002326, A122094.

Sequence in context: A347358 A333200 A229607 * A292473 A269253 A084047

Adjacent sequences: A137329 A137330 A137331 * A137333 A137334 A137335

Keyword

nonn

Author

Joerg Arndt, Apr 07 2008

Extensions

Definition revised by Max Alekseyev, May 01 2008

Status

approved