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 A102641 #12 Dec 12 2021 20:12:25
%S A102641 1,2,2,4,2,4,2,3,2,4,2,4,2,4,2,2,2,3,2,4,2,2,2,4,2,2,2,4,2,4,2,3,2,4,
%T A102641 4,4,2,3,4,4,2,3,2,4,2,2,2,4,2,3,2,4,2,4,6,2,4,2,2,3,2,3,3,2,2,3,2,3,
%U A102641 2,3,2,4,2,3,6,4,2,3,2,3,4,2,2,3,2,3,2,3,2,3,2,4,2,4,4,4,2,3,3,4,2,4,2,3,5
%N A102641 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 decreasing j.
%C A102641 A006530(2^n)=2 is a local minimum. Going either upward or downward with the argument, the largest prime factors are increasing for a while. Here the maximal length of increasing greatest-prime-factor sequences are given when going downward with the arguments. Compare with A102640.
%e A102641 For n = 12: 2^10 = 4096. The greatest prime factors of 4096, 4095, 4094, 4093 are as follows: {2, 13, 89, 4093}. A006530(4092) = 31 is already smaller than A006530(4093). Thus the length of the increasing GPF sequence is 4 = a(12).
%t A102641 With[{nn = 12}, Table[Function[k, 1 + LengthWhile[#, # > 0 &] &@ Differences@ Table[FactorInteger[m][[-1, 1]], {m, k, k - nn, -1}]][2^n], {n, 105}] ] (* _Michael De Vlieger_, Jul 24 2017 *)
%Y A102641 Cf. A006530, A102640, A102642, A102643, A102644.
%K A102641 nonn
%O A102641 1,2
%A A102641 _Labos Elemer_, Jan 21 2005