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

0,3

Links

Table of n, a(n) for n=0..105.

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

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

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 *)

Prog

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

Crossrefs

Cf. A010876, A218256.

Sequence in context: A151865 A124860 A182412 * A010704 A338947 A323503

Adjacent sequences: A038135 A038136 A038137 * A038139 A038140 A038141

Keyword

nonn,easy

Author

Felice Russo

Extensions

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

Status

approved