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

Author

Labos Elemer, Dec 09 2004

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

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

Programs

Python

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

Extensions

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