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

%I #17 Apr 04 2020 04:40:15

%S 2,3,11,5,23,11,7,83,37,29,131,179,191,43,73,239,251,359,419,431,443,

%T 491,29,659,683,233,179,719,743,911,239,1019,1031,29,1103,47,397,1223,

%U 79,461,1439,1451,1499,1511,1559,1583,557,113,431,577,601,1811,1931

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

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

%H Amiram Eldar, <a href="/A137332/b137332.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..106 from Joerg Arndt)

%F a(n) = A007733(A122094(n)) = A002326((A122094(n)-1)/2). - _Max Alekseyev_, May 01 2008

%e The k-th term of the sequence is ord(2 mod A122094(k)).

%e For example, 223 is the 9th term of A122094 and ord(2 mod 223)=37, so 37 is the 9th term of this sequence.

%e 11 is both the third term because ord(2 mod 23) == 11 and the sixth term because ord(2 mod 89) == 11.

%e Note both 23 and 89 divide 2^11-1; the third and sixth terms of A122094 are 23 and 89.

%t Select[MultiplicativeOrder[2, #] & /@ Select[Range[3, 4000, 2], PrimeQ], PrimeQ] (* _Amiram Eldar_, Apr 04 2020 *)

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

%Y Cf. A002326, A122094.

%K nonn

%O 1,1

%A _Joerg Arndt_, Apr 07 2008

%E Definition revised by _Max Alekseyev_, May 01 2008