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
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