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 A052463 #53 Feb 16 2025 08:32:42
%S A052463 0,47,2301,112747,5524601,270705447,13264566901,649963778147,
%T A052463 31848225129201,1560563031330847,76467588535211501,
%U A052463 3746911838225363547,183598680073042813801,8996335323579097876247
%N A052463 a(n) is the smallest nonnegative solution k to 24*k == 1 (mod 7^(2*n-2)).
%C A052463 Related to a Ramanujan congruence for the partition function P = A000041.
%C A052463 In other words, a(n) = k such that 24*k (mod 7^(2*n-2) ) == 1. - _N. J. A. Sloane_, Oct 08 2019
%C A052463 If b(n) = a(n) + 7^(2*n-2)*r, where r is a nonnegative integer, then there is an integer s >= 0 such that 24*b(n) = 24*a(n) + 24*7^(2*n-2)*r = 7^(2*n-2)*s + 1 + 24*7^(2*n-2)*r = 7^(2*n-2)*(24*r+s) + 1 == 1 (mod 7^(2*n-2)). Thus, we insist that a(n) is the smallest k >= 0 such that 24*k == 1 (mod 7^(2*n-2)). - _Petros Hadjicostas_, Oct 09 2019
%H A052463 Vincenzo Librandi, <a href="/A052463/b052463.txt">Table of n, a(n) for n = 1..600</a>
%H A052463 G. K. Patil, <a href="https://web.archive.org/web/20180422092157/http://www.ijsres.com/2014/vol-1_issue-6/paper_8.pdf">Ramanujan's Life And His Contributions In The Field Of Mathematics</a>, International Journal of Scientific Research and Engineering Studies (IJSRES), 1(6) (2014), ISSN: 2349-8862.
%H A052463 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>.
%H A052463 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (50,-49).
%F A052463 G.f.: x^2*(-49*x + 47)/((1 - x)*(1 - 49*x)).
%F A052463 a(n) = 49*a(n-1) - 2. - _Vincenzo Librandi_, Jul 01 2012
%F A052463 a(n) = 23*49^n/1176 + 1/24, n > 1. - _R. J. Mathar_, Oct 09 2019
%t A052463 Table[PowerMod[24, -1, 7^(2b-2)], {b, 20}]
%t A052463 CoefficientList[Series[(-49x^2+47x)/((1-x)(1-49x)),{x,0,30}],x] (* _Vincenzo Librandi_, Jul 01 2012 *)
%t A052463 LinearRecurrence[{50,-49},{0,47,2301},20] (* _Harvey P. Dale_, Aug 23 2021 *)
%o A052463 (Magma) I:=[0, 47]; [n le 2 select I[n] else 49*Self(n-1)-2: n in [1..20]]; // _Vincenzo Librandi_, Jul 01 2012
%Y A052463 Cf. A000041, A052462, A052465, A052466, A327770.
%K A052463 nonn,easy
%O A052463 1,2
%A A052463 _Eric W. Weisstein_
%E A052463 Name edited by _Petros Hadjicostas_, Oct 09 2019