A100385 - OEIS

%I #22 Nov 09 2022 19:08:34

%S 2,3,13,13,491,1851,12721,12721,109453,586951,120797465,624141002,

%T 4044619541,267793490438,315400191511,1285600699441

%N a(n) is the least number x >= 2 such that for m=x to x+n-1, A006530(m) decreases.

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

%C a(15) > 3*10^11. - _Donovan Johnson_, Oct 24 2009

%C a(17) > 7*10^12. - _Giovanni Resta_, May 04 2017

%F a(n) = A070089(x)+1, where x is the smallest positive integer such that A070089(x+1)-A070089(x) >= n. - _Pontus von Brömssen_, Nov 09 2022

%e a(5)=491 because the largest prime factors of 491,492,493,494,495 are 491,41,29,19,11.

%t Function[s, Prepend[Reverse@ FoldList[If[#2 > #1, #1, #2] &, Reverse@ #], 2] &@ Map[Function[k, First@ SelectFirst[s, And[Sign@ First@ # == 1, Length@ # == k] &]], Range[Max@ Map[Length, s]]]]@ SplitBy[Flatten[ Partition[Array[{#, FactorInteger[#][[-1, 1]]} &, 10^6], 2, 1] /. {{n_, a_}, {_, b_}} /; n > 0 :> -n Sign[Differences@ {a, b}]], Sign] (* _Michael De Vlieger_, May 04 2017, Version 10.2 *)

%Y Cf. A006530, A070087, A070089, A071870, A100384, A100386.

%K nonn,more

%O 1,1

%A _Labos Elemer_, Dec 09 2004

%E Edited by _Don Reble_, Jun 13 2007

%E a(14) from _Donovan Johnson_, Oct 24 2009

%E a(15)-a(16) from _Giovanni Resta_, May 04 2017