OFFSET
1,4
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..6561
Rémy Sigrist, Colored scatterplot of the ordinal transform of the first 3^10 terms (colored pixels correspond to n's such that a(n) is a power of 3)
FORMULA
a(3^k) = 3^(k-1) for any k > 0.
a(3^k + 1) = 3^k for any k >= 0.
a(3^k - 1) = 3^(k-1) for any k > 0.
EXAMPLE
For n = 12:
- the first powers of 3 mod 12 are:
k 3^k mod 12
-- ----------
0 1
1 3
2 9
3 3
- those values are eventually periodic, the maximum being 9,
- hence a(12) = 9.
MATHEMATICA
a[n_] := PowerMod[3, Range[0, n-1], n] // Max;
Table[a[n], {n, 1, 1000}] (* Jean-François Alcover, May 14 2023 *)
PROG
(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))) }
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Sep 21 2019
STATUS
approved