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A333334 a(n) is the smallest positive number k such that n divides 3^k + k.

%I A333334 #31 Apr 15 2020 02:24:07
%S A333334 1,1,3,1,3,3,6,5,9,3,2,9,10,15,3,13,4,9,18,17,6,29,22,21,23,17,27,25,
%T A333334 28,3,5,13,57,23,6,9,36,23,12,37,40,15,17,29,63,63,35,45,6,23,27,17,
%U A333334 19,27,57,109,18,31,10,57,52,5,90,45,17,57,66,65,63,23,70
%N A333334 a(n) is the smallest positive number k such that n divides 3^k + k.
%C A333334 For any positive integer n, if k = a(n) + n*m*A007734(n) and m >= 0 then 3^k + k is divisible by n.
%H A333334 Seiichi Manyama, <a href="/A333334/b333334.txt">Table of n, a(n) for n = 1..5000</a>
%H A333334 Brazil National Olympiad, 2005, <a href="https://artofproblemsolving.com/community/c6h57713">Problem 6</a>
%F A333334 a(3^m) = 3^m for m >= 0.
%F A333334 a(p) <= p - 1 if p is a prime greater than 3.
%t A333334 a[n_] := Module[{k = 1}, While[!Divisible[3^k + k, n], k++]; k]; Array[a, 100] (* _Amiram Eldar_, Mar 16 2020 *)
%o A333334 (PARI) a(n) = for(k=1, oo, if(Mod(3, n)^k==-k, return(k)));
%Y A333334 Cf. A007734, A247248, A333335, A333336, A333339.
%K A333334 nonn,easy
%O A333334 1,3
%A A333334 _Jinyuan Wang_, Mar 15 2020