A159008 - OEIS

%I #29 Feb 27 2024 12:08:21

%S 25,64,114,153,203,242,292,331,381,420,470,509,559,598,648,687,737,

%T 776,826,865,915,954,1004,1043,1093,1132,1182,1221,1271,1310,1360,

%U 1399,1449,1488,1538,1577,1627,1666,1716,1755,1805,1844,1894,1933,1983,2022,2072

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

%C Numbers congruent to {25, 64} mod 89. - _Amiram Eldar_, Feb 26 2023

%H Vincenzo Librandi, <a href="/A159008/b159008.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

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

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

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

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

%t LinearRecurrence[{1, 1, -1}, {25, 64, 114}, 50] (* _Vincenzo Librandi_, Mar 02 2012 *)

%t Select[Range[2100],PowerMod[#,2,89]==2&] (* _Harvey P. Dale_, May 09 2019 *)

%o (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

%o (PARI) for(n=1, 60, print1((89+11*(-1)^(n-1)+178*(n-1))/4", ")); \\ _Vincenzo Librandi_, Mar 02 2012

%Y Cf. A159007.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jun 30 2009

%E Slightly edited by _R. J. Mathar_, Jul 26 2009