A100385 -id:A100385 - cp's OEIS frontend

A100384 a(n) = the smallest number x >= 2 such that for m = x to x + n - 1, A006530(m) increases.

2, 2, 8, 8, 90, 168, 9352, 46189, 721970, 721970, 6449639, 565062156, 11336460025, 37151747513, 256994754033

Offset: 1

Labos Elemer, Dec 09 2004

A006530(m) is the largest prime factor of m.
a(16) > 3*10^11. - Donovan Johnson, Oct 24 2009
a(16) > 10^13. - Giovanni Resta, Jul 25 2013

			a(5)=90 because the largest prime factors of 90,91,92,93,94 are 5,13,23,31,47.

Cf. A006530, A070089, A071869, A100376, A100385, A358890.

from sympy import factorint
def A100384(n):
    k, a = 2, [max(factorint(m+2)) for m in range(n)]
    while True:
        for i in range(1, n):
            if a[i-1] >= a[i]:
                break
        else:
            return k
        a = a[i:] + [max(factorint(k+j+n)) for j in range(i)]
        k += i # Chai Wah Wu, Jul 24 2017

Edited by Don Reble, Jun 13 2007
a(13)-a(15) from Donovan Johnson, Oct 24 2009
Name clarified by Peter Munn, Dec 05 2022

A100386 Numbers n such that for m=n to n+9, A006530(m) decreases.

Original entry on oeis.org

586951, 1473257, 4982941, 13565441, 24954141, 25384714, 26576686, 32026196, 35797623, 35953989, 37972276, 39048260, 51755761, 58769257, 60682681, 71342703, 77863117, 80826231, 84766857, 89768134, 98363506, 110482826, 115045547, 115898807, 120797465

Offset: 1

Labos Elemer, Dec 09 2004

nonn

A006530(n) is the largest prime factor of n.

			586951 is here because the largest prime factors of 586951..586960 are 586951,73369,21739,9467,1319,1193,1181,1091,677,29.

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A006530, A070087, A071870, A100385.

<?(Max[Differences[#]]<0&),{1},Heads->False]//Flatten (* _Harvey P. Dale, Sep 18 2016 *)

Edited by Don Reble, Jun 13 2007

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

A224693 Smallest prime p such that p > gpf(p+1) > gpf(p+2) > ... > gpf(p+n) where gpf(m) is the greatest prime factor of m.

Original entry on oeis.org

3, 13, 13, 491, 2011, 12721, 12721, 109453, 586951, 173912393, 785211341, 4044619541, 315400191511, 315400191511

Offset: 1

Michel Lagneau, Apr 15 2013

a(n) >= A100385(n+1). - Zak Seidov, Apr 17 2013

			a(4) = 491 because 491 > 41 > 29 > 19 > 11 where:
492 = 2^2*3*41;
493 = 17*29;
494 = 2*13*19;
495 = 3^2*5*11.

Cf. A006530, A100385.

with(numtheory):
for n from 1 to 20 do:
   ii:=0:
        for k from 1 to 10^7 while(ii=0) do:
        p:=ithprime(k): it:=0:
            for m from 1 to n do:
               x0:=factorset(p+m-1):n0:=nops(x0): x1:=factorset(p+m):n1:=nops(x1):
               if x0[n0] > x1[n1]
               then
               it:=it+1:
              else
              fi:
          od:
             if it=n
             then
             printf ( "%d %d \n",n,p):ii:=1:
             else
             fi:
        od:
    od:

a(10)-a(12) from Zak Seidov, Apr 17 2013

a(13)-a(14) from Donovan Johnson, Apr 26 2013

cp's OEIS Frontend

A100384 a(n) = the smallest number x >= 2 such that for m = x to x + n - 1, A006530(m) increases.

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A100386 Numbers n such that for m=n to n+9, A006530(m) decreases.

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A100387 a(n) is the largest number x such that for m=n to n+x-1, A006530(m) decreases.

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A224693 Smallest prime p such that p > gpf(p+1) > gpf(p+2) > ... > gpf(p+n) where gpf(m) is the greatest prime factor of m.

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