%I #15 Sep 08 2022 08:45:10

%S 12,20,34,42,56,64,78,86,100,108,122,130,144,152,166,174,188,196,210,

%T 218,232,240,254,262,276,284,298,306,320,328,342,350,364,372,386,394,

%U 408,416,430,438,452,460,474,482,496,504,518,526,540,548,562,570,584

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

%H Colin Barker, <a href="/A082296/b082296.txt">Table of n, a(n) for n = 1..1000</a>

%H Cino Hilliard, <a href="http://groups.msn.com/BC2LCC/page.msnw?fc_p=%2FSicurv%20%2D%20Simul%20Equ%20and%20Curve%20Fitting&amp;fc_a=0">Simultaneous Equations and Curve Fitting.</a> [broken link]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

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

%F From _Colin Barker_, Jun 09 2016: (Start)

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

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

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

%F (End)

%t Table[If[OddQ[n], 11n + 1, 11 n - 2], {n, 60}] (* _Vincenzo Librandi_, Jun 09 2016 *)

%o (PARI) anpbn(n) = { for(x=1,n, if((13^x+17^x-19)%23==0,print1(x", "))) }

%o (Magma) [IsOdd(n) select 11*n+1 else 11*n-2: n in [1..60]]; // _Vincenzo Librandi_, Jun 09 2016

%o (PARI) Vec(2*x*(6+4*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ _Colin Barker_, Jun 09 2016

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, May 10 2003