A100376 -id:A100376 - cp's OEIS frontend

A100384 a(n) = the smallest number x >= 2 such that for m = x to x + n - 1, A006530(m) increases.

2, 2, 8, 8, 90, 168, 9352, 46189, 721970, 721970, 6449639, 565062156, 11336460025, 37151747513, 256994754033

Offset: 1

Labos Elemer, Dec 09 2004

A006530(m) is the largest prime factor of m.
a(16) > 3*10^11. - Donovan Johnson, Oct 24 2009
a(16) > 10^13. - Giovanni Resta, Jul 25 2013

			a(5)=90 because the largest prime factors of 90,91,92,93,94 are 5,13,23,31,47.

Cf. A006530, A070089, A071869, A100376, A100385, A358890.

from sympy import factorint
def A100384(n):
    k, a = 2, [max(factorint(m+2)) for m in range(n)]
    while True:
        for i in range(1, n):
            if a[i-1] >= a[i]:
                break
        else:
            return k
        a = a[i:] + [max(factorint(k+j+n)) for j in range(i)]
        k += i # Chai Wah Wu, Jul 24 2017

Edited by Don Reble, Jun 13 2007
a(13)-a(15) from Donovan Johnson, Oct 24 2009
Name clarified by Peter Munn, Dec 05 2022

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.

Original entry on oeis.org

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

Labos Elemer, Dec 09 2004

nonn

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,...?

			n = 85293163: the corresponding uphill run of GPFs is (739, 5197, 6311, 7457, 8537, 1776941, 6561013, 8529317, 9477019, 21323293).

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]

Cf. A006530, A071869, A070089, A100376, A100384.

A100387 a(n) is the largest number x such that for m=n to n+x-1, A006530(m) decreases.

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 4, 3, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 1, 3, 2, 1, 2, 1, 1, 1, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1

Offset: 2

Labos Elemer, Dec 10 2004

nonn

A006530(m) is the largest prime factor of m.

			a(13)=4 because the largest prime factors of 13,14,15,16 are 13,7,5,2; but A006530(17)=17.

Cf. A006530, A070087, A070089, A071870, A079748, A100376, A100385, A100386.

Mathematica
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From Pontus von Brömssen, Nov 09 2022: (Start)
a(n) = 1 if and only if n >= 2 and n is a term of A070089.
If a(n) > 1 then a(n) = a(n+1)+1.
(End)

Edited by Don Reble, Jun 13 2007

cp's OEIS Frontend

A100384 a(n) = the smallest number x >= 2 such that for m = x to x + n - 1, A006530(m) increases.

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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.

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Crossrefs

A100387 a(n) is the largest number x such that for m=n to n+x-1, A006530(m) decreases.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions