A100386 -id:A100386 - cp's OEIS frontend

A100385 a(n) is the least number x >= 2 such that for m=x to x+n-1, A006530(m) decreases.

2, 3, 13, 13, 491, 1851, 12721, 12721, 109453, 586951, 120797465, 624141002, 4044619541, 267793490438, 315400191511, 1285600699441

Offset: 1

Labos Elemer, Dec 09 2004

A006530(m) is the largest prime factor of m.
a(15) > 3*10^11. - Donovan Johnson, Oct 24 2009
a(17) > 7*10^12. - Giovanni Resta, May 04 2017

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

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

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 *)

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

Edited by Don Reble, Jun 13 2007
a(14) from Donovan Johnson, Oct 24 2009
a(15)-a(16) from Giovanni Resta, May 04 2017

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

A100385 a(n) is the least number x >= 2 such that for m=x to x+n-1, A006530(m) decreases.

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