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A327650 Maximum value of powers of 3 mod n.

%I A327650 #24 May 14 2023 09:05:58
%S A327650 0,1,1,3,4,3,6,3,3,9,9,9,9,13,12,11,16,9,18,9,18,15,18,9,24,9,9,27,28,
%T A327650 27,30,27,27,33,33,27,36,37,27,27,40,39,42,37,36,41,42,33,48,49,48,35,
%U A327650 52,27,53,27,54,57,57,27,60,61,54,59,61,45,66,63,54,51
%N A327650 Maximum value of powers of 3 mod n.
%H A327650 Rémy Sigrist, <a href="/A327650/b327650.txt">Table of n, a(n) for n = 1..6561</a>
%H A327650 Rémy Sigrist, <a href="/A327650/a327650.png">Colored scatterplot of the ordinal transform of the first 3^10 terms</a> (colored pixels correspond to n's such that a(n) is a power of 3)
%F A327650 a(3^k) = 3^(k-1) for any k > 0.
%F A327650 a(3^k + 1) = 3^k for any k >= 0.
%F A327650 a(3^k - 1) = 3^(k-1) for any k > 0.
%e A327650 For n = 12:
%e A327650 - the first powers of 3 mod 12 are:
%e A327650     k   3^k mod 12
%e A327650     --  ----------
%e A327650      0           1
%e A327650      1           3
%e A327650      2           9
%e A327650      3           3
%e A327650 - those values are eventually periodic, the maximum being 9,
%e A327650 - hence a(12) = 9.
%t A327650 a[n_] := PowerMod[3, Range[0, n-1], n] // Max;
%t A327650 Table[a[n], {n, 1, 1000}] (* _Jean-François Alcover_, May 14 2023 *)
%o A327650 (PARI) a(n) = { my (p=1%n, mx=p); while (1, p=(3*p)%n; if (mx<p, mx=p, mx==p || p==0, return (mx))) }
%Y A327650 Cf. A000244, A327649.
%K A327650 nonn
%O A327650 1,4
%A A327650 _Rémy Sigrist_, Sep 21 2019