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.

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

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