A159008 Positive numbers k such that k^2 == 2 (mod 89).

25, 64, 114, 153, 203, 242, 292, 331, 381, 420, 470, 509, 559, 598, 648, 687, 737, 776, 826, 865, 915, 954, 1004, 1043, 1093, 1132, 1182, 1221, 1271, 1310, 1360, 1399, 1449, 1488, 1538, 1577, 1627, 1666, 1716, 1755, 1805, 1844, 1894, 1933, 1983, 2022, 2072

Offset

1,1

Comments

Numbers congruent to {25, 64} mod 89. - 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).

Formula

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

G.f.: x*(25 + 39*x + 25*x^2)/((1+x)*(x-1)^2).

a(n) = (89 + 11*(-1)^(n-1) + 178*(n-1))/4.

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(39*Pi/178)*Pi/89. - Amiram Eldar, Feb 26 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {25, 64, 114}, 50] (* Vincenzo Librandi, Mar 02 2012 *)
Select[Range[2100], PowerMod[#, 2, 89]==2&] (* Harvey P. Dale, May 09 2019 *)

Prog

(Magma) I:=[25, 64, 114]; [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
(PARI) for(n=1, 60, print1((89+11*(-1)^(n-1)+178*(n-1))/4", ")); \\ Vincenzo Librandi, Mar 02 2012

Crossrefs

Cf. A159007.

Sequence in context: A211326 A103645 A061970 * A183373 A354381 A306358

Adjacent sequences: A159005 A159006 A159007 * A159009 A159010 A159011

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 30 2009

Extensions

Slightly edited by R. J. Mathar, Jul 26 2009

Status

approved