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

%I A100376 #15 Oct 19 2017 03:14:36
%S A100376 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,
%T A100376 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,
%U A100376 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
%N A100376 a(n) is the largest number x such that for m=n to n+x-1, A006530(m) increases.
%C A100376 A006530(m) is the greatest prime factor (gpf) of m.
%C A100376 If p is an odd prime, a(p)=1, because the largest prime factor of p+1 is smaller than p.
%H A100376 Michel Marcus, <a href="/A100376/b100376.txt">Table of n, a(n) for n = 2..10000</a>
%e A100376 a(8)=4 because the largest prime factors of 8,9,10,11 are 2,3,5,11; but gpf(12)=3.
%e A100376 From _Michael De Vlieger_, Jul 30 2017: (Start)
%e A100376 Value  First position
%e A100376    1         3
%e A100376    2         2
%e A100376    3         9
%e A100376    4         8
%e A100376    5        90
%e A100376    6       168
%e A100376    7      9352
%e A100376    8     46189
%e A100376    9    721971
%e A100376   10    721970
%e A100376 (End)
%t A100376 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 *)
%o A100376 (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
%Y A100376 Cf. A006530, A070089, A071869, A100384, A100387.
%K A100376 nonn
%O A100376 2,1
%A A100376 _Labos Elemer_, Dec 09 2004
%E A100376 Edited by _Don Reble_, Jun 13 2007