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A143663 a(n) is the least prime such that the multiplicative order of 3 mod a(n) equals n, or a(n)=1 if no such prime exists.

%I A143663 #31 Dec 28 2024 16:19:01
%S A143663 2,1,13,5,11,7,1093,41,757,61,23,73,797161,547,4561,17,1871,19,1597,
%T A143663 1181,368089,67,47,6481,8951,398581,109,29,59,31,683,21523361,
%U A143663 2413941289,103,71,530713,13097927,2851,313,42521761,83,43,431,5501,181,23535794707
%N A143663 a(n) is the least prime such that the multiplicative order of 3 mod a(n) equals n, or a(n)=1 if no such prime exists.
%C A143663 If a(n) differs from 1, then a(n) is the minimal prime divisor of A064079(n).
%H A143663 Max Alekseyev, <a href="/A143663/b143663.txt">Table of n, a(n) for n = 1..730</a> (first 153 terms from Robert G. Wilson v)
%p A143663 a:= proc(n) local f,p;
%p A143663 f:= numtheory:-factorset(3^n - 1);
%p A143663 for  p in f do
%p A143663    if numtheory:-order(3,p) = n then return p fi
%p A143663 od:
%p A143663 1
%p A143663 end proc:
%p A143663 seq(a(n),n=1..100); # _Robert Israel_, Oct 13 2014
%t A143663 p = 2; t = Table[0, {100}]; While[p < 100000001, a = MultiplicativeOrder[3, p]; If[0 < a < 101 && t[[a]] == 0, t[[a]] = p; Print[{a, p}]];  p = NextPrime@ p]; t (* _Robert G. Wilson v_, Oct 13 2014 *)
%Y A143663 Cf. A002326, A064079, A112092, A218356, A057958, A074477.
%Y A143663 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).
%K A143663 nonn
%O A143663 1,1
%A A143663 _Vladimir Shevelev_, Aug 28 2008
%E A143663 More terms from _Robert G. Wilson v_, Dec 11 2013