A092476 Numbers that are congruent to {1, 3, 9} mod 13.

1, 3, 9, 14, 16, 22, 27, 29, 35, 40, 42, 48, 53, 55, 61, 66, 68, 74, 79, 81, 87, 92, 94, 100, 105, 107, 113, 118, 120, 126, 131, 133, 139, 144, 146, 152, 157, 159, 165, 170, 172, 178, 183, 185, 191, 196, 198, 204, 209, 211, 217, 222, 224, 230, 235, 237, 243, 248

Offset

1,2

Comments

Also, natural numbers whose cubes are congruent to 1 (mod 13).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

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

Formula

From R. J. Mathar, Apr 20 2009: (Start)

G.f.: x*(1+2*x+6*x^2+4*x^3)/((1+x+x^2)*(x-1)^2).

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = a(n-3) + 13 for n>3. (End)

From Wesley Ivan Hurt, Jun 09 2016: (Start)

a(n) = (39*n-39+3*cos(2*n*Pi/3)+7*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 13k-4, a(3k-1) = 13k-10, a(3k-2) = 13k-12. (End)

Maple

A092476:=n->(39*n-39+3*cos(2*n*Pi/3)+7*sqrt(3)*sin(2*n*Pi/3))/9: seq(A092476(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 300], MemberQ[{1, 3, 9}, Mod[#, 13]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)
Table[13 n + {1, 3, 9}, {n, 0, 200}]//Flatten (* Vincenzo Librandi, Jun 11 2016 *)

Prog

(PARI) for (i=1, 500, if(Mod(i^3, 13)==1, print1(i, ", ")))
(Magma) [n : n in [0..150] | n mod 13 in [1, 3, 9]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A134904 A358271 A310324 * A291641 A071346 A103813

Adjacent sequences: A092473 A092474 A092475 * A092477 A092478 A092479

Keyword

nonn,easy

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 25 2004

Extensions

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr) and Ray Chandler, Mar 26 2004

Better definition from Ralf Stephan, Dec 02, 2004

Status

approved