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 A100383 #14 Dec 12 2021 20:11:20 %S A100383 721970,1091150,6449639,6449640,10780550,12161824,15571630,17332430, %T A100383 23189750,24901256,28262037,30275508,30814114,32184457,32608598, %U A100383 35323087,35725704,38265227,38896955,69845438,71040720,74345936,79910528,85293163,111082114 %N A100383 Numbers k such that gpf(k) < gpf(k+1) < ... < gpf(k+9), where gpf(x) = A006530(x), the greatest prime factor of x. Numbers initiating an uphill gpf run of length 10. %C A100383 Analogous chains of length 3 (see A071869) are infinite as shown by Erdős and Pomerance (1978). What is true for longer successions of length=4,5,...? %H A100383 Donovan Johnson, <a href="/A100383/b100383.txt">Table of n, a(n) for n = 1..1000</a> %H A100383 P. Erdős and C. Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/PDF/paper17.pdf">On the largest prime factors of n and n+1</a>, Aequationes Math. 17 (1978), pp. 311-321. [<a href="http://www.renyi.hu/~p_erdos/1978-29.pdf">alternate link</a>] %e A100383 n = 85293163: the corresponding uphill run of GPFs is (739, 5197, 6311, 7457, 8537, 1776941, 6561013, 8529317, 9477019, 21323293). %Y A100383 Cf. A006530, A071869, A070089, A100376, A100384. %K A100383 nonn %O A100383 1,1 %A A100383 _Labos Elemer_, Dec 09 2004