login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A112092
a(n) is the least prime such that the multiplicative order of 4 mod a(n) equals n.
5
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..1122 (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
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