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

1,1

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)

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 *)

Prog

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

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).

Sequence in context: A078683 A395102 A099863 * A031441 A078150 A276044

Adjacent sequences: A112089 A112090 A112091 * A112093 A112094 A112095

Keyword

nonn

Author

Vladimir Shevelev, Aug 28 2008

Extensions

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

More term from Amiram Eldar, Jan 27 2019

Status

approved