A113541 Numbers k such that 18*k^2+1 is multiple of 19.

1, 18, 20, 37, 39, 56, 58, 75, 77, 94, 96, 113, 115, 132, 134, 151, 153, 170, 172, 189, 191, 208, 210, 227, 229, 246, 248, 265, 267, 284, 286, 303, 305, 322, 324, 341, 343, 360, 362, 379, 381, 398, 400, 417, 419, 436, 438, 455, 457, 474, 476, 493, 495, 512

Offset

1,2

Comments

Numbers congruent to {1, 18} mod 19. - Amiram Eldar, Feb 27 2023

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

a(1)=1, a(2)=18 then add alternatively 2 and 17.

a(n) = 19*(n-1) - a(n-1), (with a(1)=1). - Vincenzo Librandi, Nov 13 2010

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(Pi/19)*Pi/19. - Amiram Eldar, Feb 27 2023

Mathematica

s={}; Do[If[IntegerQ[(18n^2+1)/19], AppendTo[s, n]], {n, 200}]; s

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, 1, 1]^(n-1)*[1; 18; 20])[1, 1] \\ Charles R Greathouse IV, Jul 08 2024

Crossrefs

Sequence in context: A335897 A036170 A064271 * A181453 A113542 A075865

Adjacent sequences: A113538 A113539 A113540 * A113542 A113543 A113544

Keyword

nonn,easy

Author

Zak Seidov, Jan 13 2006

Extensions

a(22)-a(56) from Vincenzo Librandi, Oct 23 2009

Status

approved