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A082296 Solutions to 13^x+17^x == 19 mod 23. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 12 23:09 EDT 2021. Contains 343829 sequences. (Running on oeis4.)