A038138 Order of n (mod 7).

0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0, 1, 3, 6, 3, 6, 2, 0

Offset: 0

Author

Felice Russo

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Crossrefs

Cf. A010876, A218256.

Programs

Magma

[Modorder(n,7): n in [0..110]]; // Bruno Berselli, Mar 22 2016

Mathematica

ReplacePart[Table[MultiplicativeOrder[n, 7], {n, 105}], List /@ Range[7, 105, 7] -> 0] (* Alonso del Arte, Mar 23 2016 *)
PadRight[{},120,{0,1,3,6,3,6,2}] (* Harvey P. Dale, Apr 26 2020 *)

PARI

a(n) = if (n % 7, znorder(Mod(n, 7)), 0); \\ Michel Marcus, Mar 22 2016

PARI

x='x+O('x^200); concat(0, Vec(x*(1+3*x+6*x^2+3*x^3+6*x^4+2*x^5)/(1-x^7))) \\ Altug Alkan, Mar 23 2016

Formula

G.f.: x*(1 + 3*x + 6*x^2 + 3*x^3 + 6*x^4 + 2*x^5)/(1 - x^7). - Bruno Berselli, Mar 22 2016

a(n) = -(35*(n mod 7)^6 - 603*(n mod 7)^5 + 3860*(n mod 7)^4 - 11235*(n mod 7)^3 + 14465*(n mod 7)^2 - 6882*(n mod 7))/360. - Luce ETIENNE, Oct 20 2017

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 04 2000