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 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. 1
 721970, 1091150, 6449639, 6449640, 10780550, 12161824, 15571630, 17332430, 23189750, 24901256, 28262037, 30275508, 30814114, 32184457, 32608598, 35323087, 35725704, 38265227, 38896955, 69845438, 71040720, 74345936, 79910528, 85293163, 111082114 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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,...? LINKS Donovan Johnson, Table of n, a(n) for n = 1..1000 P. Erdős and C. Pomerance, On the largest prime factors of n and n+1, Aequationes Math. 17 (1978), pp. 311-321. [alternate link] EXAMPLE n = 85293163: the corresponding uphill run of GPFs is (739, 5197, 6311, 7457, 8537, 1776941, 6561013, 8529317, 9477019, 21323293). CROSSREFS Cf. A006530, A071869, A070089, A100376, A100384. Sequence in context: A190932 A153580 A153581 * A250153 A252324 A204150 Adjacent sequences:  A100380 A100381 A100382 * A100384 A100385 A100386 KEYWORD nonn AUTHOR Labos Elemer, Dec 09 2004 STATUS approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)