A112092 a(n) is the least prime such that the multiplicative order of 4 mod a(n) equals n.

3, 5, 7, 17, 11, 13, 43, 257, 19, 41, 23, 241, 2731, 29, 151, 65537, 43691, 37, 174763, 61681, 337, 397, 47, 97, 251, 53, 87211, 15790321, 59, 61, 715827883, 641, 67, 137, 71, 433, 223, 229, 79, 4278255361, 83, 1429, 431, 353, 631, 277, 283, 193, 4363953127297

Offset: 1

Author

Vladimir Shevelev, Aug 28 2008

Keywords

• nonn

Comments

a(n) is the minimal prime divisor of A064080(n).

Links

• Max Alekseyev, Table of n, a(n) for n = 1..1207 (first 100 terms from Amiram Eldar)

Crossrefs

Cf. A064080, A112927.

Cf. A112927 (base 2), A143663 (base 3), A112092 (base 4), A143665 (base 5), A379639 (base 6), A379640 (base 7), A379641 (base 8), A379642 (base 9), A007138 (base 10), A379644 (base 11), A252170 (base 12).

Programs

Mathematica

a[n_] := Module[{f = FactorInteger[4^n - 1][[;; , 1]]}, Do[p = f[[k]]; If[ MultiplicativeOrder[4, p] == n, Break[] ], {k, 1, Length[f]}]; p]; Array[a, 100] (* Amiram Eldar, Jan 27 2019 *)

PARI

a(n) = {my(p = 3); while (znorder(Mod(4, p)) != n, p = nextprime(p+1)); p;} \\ Michel Marcus, Feb 08 2016

Extensions

a(29)-a(30) from Michel Marcus, Feb 08 2016

More term from Amiram Eldar, Jan 27 2019