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 A255595 #27 Sep 08 2020 14:36:35
%S A255595 2,3,7,43,63,92,89,94,23,71,66,40,35,101,73,25,56,29,50,53,32,12,24,8,
%T A255595 57,32,12,24,8,57,32,12,24,8,57,32,12,24,8,57,32,12,24,8,57,32,12,24,
%U A255595 8,57,32,12,24,8,57,32,12,24,8,57,32,12,24,8,57,32,12,24,8,57,32,12,24,8,57,32
%N A255595 Sylvester's sequence modulo 109.
%C A255595 For most small primes, it's easy to see that they have no multiples in Sylvester's sequence (A000058) by considering the sequence modulo the prime in question. For example, Sylvester's sequence modulo 41 is 2, 3, 7, 2, 3, 7, 2, 3, 7, ...
%C A255595 But with 109, it isn't until A000058(25) modulo 109 that we encounter the repeated value of 32. From this point forward, the period {32, 12, 24, 8, 57} is infinitely repeated. The table in Sylvester (1880) is missing the 57.
%D A255595 J. J. Sylvester, Postscript to Note on a Point in Vulgar Fractions. American Journal of Mathematics Vol. 3, No. 4 (Dec., 1880): 389, Table.
%H A255595 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F A255595 a(0) = 2, a(n) = a(n - 1)^2 - a(n - 1) + 1 mod 109.
%e A255595 a(4) = 43 because a(3) = 7 and 7^2 - 7 + 1 = 43.
%e A255595 a(5) = 63 because 43^2 - 43 + 1 = 1807 = 63 mod 109.
%t A255595 sylv109[0] := 2; sylv109[n_] := sylv109[n] = Mod[sylv109[n - 1](sylv109[n - 1] - 1) + 1, 109]; Table[sylv109[n], {n, 0, 108}]
%t A255595 PadRight[{2,3,7,43,63,92,89,94,23,71,66,40,35,101,73,25,56,29,50,53},120,{32,12,24,8,57}] (* _Harvey P. Dale_, Sep 08 2020 *)
%K A255595 nonn,easy
%O A255595 0,1
%A A255595 _Alonso del Arte_, Mar 25 2015