This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A155107 #34 Feb 22 2025 18:28:01
%S A155107 23,30,76,83,129,136,182,189,235,242,288,295,341,348,394,401,447,454,
%T A155107 500,507,553,560,606,613,659,666,712,719,765,772,818,825,871,878,924,
%U A155107 931,977,984,1030,1037,1083,1090,1136,1143,1189,1196,1242,1249,1295
%N A155107 Numbers that are 23 or 30 (mod 53).
%C A155107 Also, numbers k such that k^2 == -1 (mod 53).
%C A155107 The first pair (a,b) is such that a+b=p=53, a*b=p*h+1, with h<=(p-1)/4; subsequent pairs are given as (a+kp, b+kp), k=1,2,3...
%H A155107 Vincenzo Librandi, <a href="/A155107/b155107.txt">Table of n, a(n) for n = 1..1000</a>
%H A155107 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A155107 a(n) = 23*(-1)^(n+1) + 53*floor(n/2). - _M. F. Hasler_, Jun 16 2010
%F A155107 a(2k+1) = 53 k + a(1), a(2k) = 53 k - a(1), with a(1) = 23 = A002314(7) since 53 = A002144(7). - _M. F. Hasler_, Jun 16 2010
%F A155107 a(n) = a(n-2) + 53 for all n > 2. - _M. F. Hasler_, Jun 16 2010
%F A155107 From _R. J. Mathar_, Feb 19 2009: (Start)
%F A155107 a(n) = a(n-1) + a(n-2) - a(n-3) = 53*n/2 - 53/4 - 39*(-1)^n/4.
%F A155107 G.f.: x*(23 + 7*x + 23*x^2)/((1+x)*(1-x)^2). (End)
%t A155107 Select[Range[1300], PowerMod[#, 2, 53] == 52 &] (* or *) LinearRecurrence[ {1, 1, -1}, {23, 30, 76}, 50] (* _Harvey P. Dale_, Nov 30 2011 *)
%t A155107 CoefficientList[Series[(23 + 7 x + 23 x^2)/((1 + x) (1 - x)^2), {x, 0, 100}], x] (* _Vincenzo Librandi_, Apr 24 2014 *)
%o A155107 (PARI) A155107(n)=n\2*53-23*(-1)^n /* _M. F. Hasler_, Jun 16 2010 */
%o A155107 (Magma) I:=[23,30,76]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Apr 24 2014
%o A155107 (Magma) [-23*(-1)^n+53*Floor(n/2): n in [1..50]]; // _Vincenzo Librandi_, Apr 24 2014
%Y A155107 Cf. numbers n such that n^2 == -1 (mod p), where p is a prime of the form 4k+1: A047221 (p=5), A155086 (p=13), A155095 (p=17), A155096 (p=29), A155097 (p=37), A155098 (p=41), this sequence (p=53), A241406 (p=61), A241407 (p=73), A241520 (p=89), A241521 (p=97).
%K A155107 nonn,easy
%O A155107 1,1
%A A155107 _Vincenzo Librandi_, Jan 20 2009
%E A155107 Terms checked & minor edits by _M. F. Hasler_, Jun 16 2010