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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.
2
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
Sequence in context: A347358 A333200 A229607 * A292473 A269253 A084047
KEYWORD
nonn
AUTHOR
Joerg Arndt, Apr 07 2008
EXTENSIONS
Definition revised by Max Alekseyev, May 01 2008
STATUS
approved