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 A102640 #14 Dec 12 2021 20:12:11
%S A102640 2,2,4,2,3,2,2,2,3,2,2,4,2,3,2,2,3,4,2,3,3,6,2,3,2,4,2,2,3,4,2,3,3,2,
%T A102640 2,4,2,4,2,2,2,4,2,3,4,4,2,4,2,3,3,2,2,3,2,2,3,2,2,2,2,3,2,2,3,4,2,3,
%U A102640 4,4,2,4,2,3,2,2,4,4,2,3,3,4,2,2,2,3,2,4,2,3,2,2,3,2,2,2,3,4,2,4,2,3,2,2,3
%N A102640 Compute the greatest prime factors (GPFs, A006530()) of j + 2^n for j = 0, 1, ..., L. a(n) is the maximal length L of such a sequence in which the greatest prime factors are increasing with increasing j.
%C A102640 A006530(2^n)=2 is a local minimum. Going either upward or downward with the argument, the greatest prime factors are increasing for a while.
%e A102640 For n = 12: 2^10 = 4096. The greatest prime factors of 4096, 4097, 4098, 4099 are as follows: {2, 241, 683, 4099}. A006530(4100) = 41 is already smaller than A006530(4099). Thus the length of increasing GPF sequence is 4 = a(12).
%t A102640 With[{nn = 12}, Table[Function[k, 1 + LengthWhile[#, # > 0 &] &@ Differences@ Array[FactorInteger[#][[-1, 1]] &, nn, k]][2^n], {n, 105}]] (* _Michael De Vlieger_, Jul 24 2017 *)
%Y A102640 Cf. A006530, A102641, A102642, A102643, A102644.
%K A102640 nonn
%O A102640 1,1
%A A102640 _Labos Elemer_, Jan 21 2005