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.

2, 1, 13, 5, 11, 7, 1093, 41, 757, 61, 23, 73, 797161, 547, 4561, 17, 1871, 19, 1597, 1181, 368089, 67, 47, 6481, 8951, 398581, 109, 29, 59, 31, 683, 21523361, 2413941289, 103, 71, 530713, 13097927, 2851, 313, 42521761, 83, 43, 431, 5501, 181, 23535794707

Offset

1,1

Comments

If a(n) differs from 1, then a(n) is the minimal prime divisor of A064079(n).

Links

Max Alekseyev, Table of n, a(n) for n = 1..730 (first 153 terms from Robert G. Wilson v)

Maple

a:= proc(n) local f, p;
f:= numtheory:-factorset(3^n - 1);
for  p in f do
   if numtheory:-order(3, p) = n then return p fi
od:
1
end proc:
seq(a(n), n=1..100); # Robert Israel, Oct 13 2014

Mathematica

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 *)

Crossrefs

Cf. A002326, A064079, A112092, A218356, A057958, A074477.

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: A352571 A245625 A292947 * A064079 A167584 A112226

Adjacent sequences: A143660 A143661 A143662 * A143664 A143665 A143666

Keyword

nonn

Author

Vladimir Shevelev, Aug 28 2008

Extensions

More terms from Robert G. Wilson v, Dec 11 2013

Status

approved