A327650 Maximum value of powers of 3 mod n.

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, 27, 30, 27, 27, 33, 33, 27, 36, 37, 27, 27, 40, 39, 42, 37, 36, 41, 42, 33, 48, 49, 48, 35, 52, 27, 53, 27, 54, 57, 57, 27, 60, 61, 54, 59, 61, 45, 66, 63, 54, 51

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

Cf. A000244, A327649.

Sequence in context: A238161 A332880 A281626 * A338128 A242801 A021295

Adjacent sequences: A327647 A327648 A327649 * A327651 A327652 A327653

Keyword

nonn

Author

Rémy Sigrist, Sep 21 2019

Status

approved