A164131 Numbers k such that k^2 == 2 (mod 31).

8, 23, 39, 54, 70, 85, 101, 116, 132, 147, 163, 178, 194, 209, 225, 240, 256, 271, 287, 302, 318, 333, 349, 364, 380, 395, 411, 426, 442, 457, 473, 488, 504, 519, 535, 550, 566, 581, 597, 612, 628, 643, 659, 674, 690, 705, 721, 736, 752, 767, 783, 798, 814

Offset

1,1

Comments

Sequences of the type n^2 == 2 (mod m) are basically defined for each m of A057126. See A047341 (m=7), A113804 (m=14), A155449 (m=17), A155450 (m=23), A158803 (m=41) etc. - R. J. Mathar, Aug 26 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

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

a(n) = (31+(-1)^(n-1)+62(n-1))/4.

G.f.: x*(8+15*x+8*x^2)/((1+x)*(x-1)^2). - R. J. Mathar, Aug 26 2009

a(n) = 31*(n-1)-a(n-1) with n>1, a(1)=8. - Vincenzo Librandi, Nov 30 2010

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(15*Pi/62)*Pi/31. - Amiram Eldar, Feb 28 2023

Example

At n= 4, a(4)=(31-1+186)/4=54. At n=5, a(5)=(31+1+248)/4=70.

Mathematica

Select[Range[850], Mod[#^2, 31]==2&]  (* Harvey P. Dale, Feb 04 2011 *)

Prog

(PARI) isok(k) = Mod(k, 31)^2 == 2; \\ Michel Marcus, Nov 22 2022

Crossrefs

Cf. A057126, A047341, A113804, A155449, A155450, A158803.

Sequence in context: A345833 A164284 A047719 * A212458 A114381 A139433

Adjacent sequences: A164128 A164129 A164130 * A164132 A164133 A164134

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 11 2009

Extensions

Entries checked by R. J. Mathar, Aug 26 2009

Status

approved