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

%I A137332 #17 Apr 04 2020 04:40:15
%S A137332 2,3,11,5,23,11,7,83,37,29,131,179,191,43,73,239,251,359,419,431,443,
%T A137332 491,29,659,683,233,179,719,743,911,239,1019,1031,29,1103,47,397,1223,
%U A137332 79,461,1439,1451,1499,1511,1559,1583,557,113,431,577,601,1811,1931
%N A137332 Primes which are equal to the order of 2 modulo a prime q, sorted with respect to the value of q.
%C A137332 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 A137332 Amiram Eldar, <a href="/A137332/b137332.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..106 from Joerg Arndt)
%F A137332 a(n) = A007733(A122094(n)) = A002326((A122094(n)-1)/2). - _Max Alekseyev_, May 01 2008
%e A137332 The k-th term of the sequence is ord(2 mod A122094(k)).
%e A137332 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 A137332 11 is both the third term because ord(2 mod 23) == 11 and the sixth term because ord(2 mod 89) == 11.
%e A137332 Note both 23 and 89 divide 2^11-1; the third and sixth terms of A122094 are 23 and 89.
%t A137332 Select[MultiplicativeOrder[2, #] & /@ Select[Range[3, 4000, 2], PrimeQ], PrimeQ] (* _Amiram Eldar_, Apr 04 2020 *)
%o A137332 (PARI) forprime (p=3, 10^4, r = znorder( Mod(2,p) ); if ( isprime(r), print1(r, ", "); ); );
%Y A137332 Cf. A002326, A122094.
%K A137332 nonn
%O A137332 1,1
%A A137332 _Joerg Arndt_, Apr 07 2008
%E A137332 Definition revised by _Max Alekseyev_, May 01 2008