A158803 Numbers k such that k^2 == 2 (mod 41).

17, 24, 58, 65, 99, 106, 140, 147, 181, 188, 222, 229, 263, 270, 304, 311, 345, 352, 386, 393, 427, 434, 468, 475, 509, 516, 550, 557, 591, 598, 632, 639, 673, 680, 714, 721, 755, 762, 796, 803, 837, 844, 878, 885, 919, 926, 960, 967, 1001, 1008, 1042, 1049

Offset: 1

Author

Vincenzo Librandi, Mar 27 2009

Keywords

• nonn
• easy

Comments

Numbers congruent to {17, 24} mod 41. - Amiram Eldar, Feb 26 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

I:=[17, 24, 58]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Mar 02 2012

Mathematica

LinearRecurrence[{1, 1, -1}, {17, 24, 58}, 60] (* Vincenzo Librandi, Mar 02 2012 *)
Select[Range[1200],PowerMod[#,2,41]==2&] (* Harvey P. Dale, Oct 24 2021 *)

PARI

a(n) = (1/4)*(41+27*(-1)^(n-1)+82*(n-1)); \\ Vincenzo Librandi, Mar 02 2012

Formula

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

a(n) = (1/4)*(41 + 27*(-1)^(n-1) + 82*(n-1)).

First differences: a(2n) - a(2n-1) = 7, a(2n+1) - a(2n) = 34.

G.f.: x*(17 + 7*x + 17*x^2)/((1+x)*(x-1)^2). - R. J. Mathar, Apr 04 2009

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(7*Pi/82)*Pi/41. - Amiram Eldar, Feb 26 2023

Extensions

Comments translated to formulas by R. J. Mathar, Apr 04 2009