A100376 a(n) is the largest number x such that for m=n to n+x-1, A006530(m) increases.

2, 1, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 3, 2, 1, 3, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 3, 2, 1, 3, 2, 1, 1, 2, 1, 5, 4, 3, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 3

Offset

2,1

Comments

A006530(m) is the greatest prime factor (gpf) of m.

If p is an odd prime, a(p)=1, because the largest prime factor of p+1 is smaller than p.

Links

Michel Marcus, Table of n, a(n) for n = 2..10000

Example

a(8)=4 because the largest prime factors of 8,9,10,11 are 2,3,5,11; but gpf(12)=3.
From Michael De Vlieger, Jul 30 2017: (Start)
Value  First position
   1         3
   2         2
   3         9
   4         8
   5        90
   6       168
   7      9352
   8     46189
   9    721971
  10    721970
(End)

Mathematica

With[{s = Differences@ Array[FactorInteger[#][[-1, 1]] &, 115]}, Table[1 + LengthWhile[Drop[s, n], # > 0 &], {n, Length@ s - 10}]] (* Michael De Vlieger, Jul 30 2017 *)

Prog

(PARI) a(n) = {m = n+1; gpf = vecmax(factor(n)[, 1]); while((ngpf=vecmax(factor(m)[, 1])) > gpf, m++; gpf = ngpf; ); m - n; } \\ Michel Marcus, Jul 25 2017

Crossrefs

Cf. A006530, A070089, A071869, A100384, A100387.

Sequence in context: A161272 A160976 A029218 * A336318 A020738 A063279

Adjacent sequences: A100373 A100374 A100375 * A100377 A100378 A100379

Keyword

nonn

Author

Labos Elemer, Dec 09 2004

Extensions

Edited by Don Reble, Jun 13 2007

Status

approved