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

1,1

Comments

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

Links

Table of n, a(n) for n=1..16.

Formula

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

Example

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

Mathematica

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 *)

Crossrefs

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

Sequence in context: A117684 A056445 A171483 * A250184 A128460 A273617

Adjacent sequences: A100382 A100383 A100384 * A100386 A100387 A100388

Keyword

nonn,more

Author

Labos Elemer, Dec 09 2004

Extensions

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

Status

approved