A082296 Solutions to 13^x+17^x == 19 mod 23.

12, 20, 34, 42, 56, 64, 78, 86, 100, 108, 122, 130, 144, 152, 166, 174, 188, 196, 210, 218, 232, 240, 254, 262, 276, 284, 298, 306, 320, 328, 342, 350, 364, 372, 386, 394, 408, 416, 430, 438, 452, 460, 474, 482, 496, 504, 518, 526, 540, 548, 562, 570, 584

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Cino Hilliard, Simultaneous Equations and Curve Fitting. [broken link]

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

Formula

Numbers of the form 11*n+1 with n odd or 11*n-2 with n even.

From Colin Barker, Jun 09 2016: (Start)

a(n) = (-1-3*(-1)^n+22*n)/2.

a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.

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

(End)

Mathematica

Table[If[OddQ[n], 11n + 1, 11 n - 2], {n, 60}] (* Vincenzo Librandi, Jun 09 2016 *)

Prog

(PARI) anpbn(n) = { for(x=1, n, if((13^x+17^x-19)%23==0, print1(x", "))) }
(Magma) [IsOdd(n) select 11*n+1 else 11*n-2: n in [1..60]]; // Vincenzo Librandi, Jun 09 2016
(PARI) Vec(2*x*(6+4*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Colin Barker, Jun 09 2016

Crossrefs

Sequence in context: A082800 A026041 A299028 * A187766 A260905 A211415

Adjacent sequences: A082293 A082294 A082295 * A082297 A082298 A082299

Keyword

easy,nonn

Author

Cino Hilliard, May 10 2003

Status

approved