A079748 -id:A079748 - cp's OEIS frontend

A358890 a(n) is the first term of the first maximal run of n consecutive numbers with increasing greatest prime factors.

14, 4, 1, 8, 90, 168, 9352, 46189, 2515371, 721970, 6449639, 565062156, 11336460025, 37151747513, 256994754033, 14037913234203

Offset: 1

Reinhard Zumkeller, Jan 10 2003

a(16) > 10^13. - Giovanni Resta, Jul 25 2013
The convention gpf(1) = A006530(1) = 1 is used (otherwise we would have a(2) = 2 and a(3) = 24). - Pontus von Brömssen, Dec 05 2022
a(17) > 10^14. - Martin Ehrenstein, Dec 10 2022

			a(7) = 9352 because the first sequence of seven consecutive numbers with increasing greatest prime factors is 9352=167*7*2^3, 9353=199*47, 9354=1559*3*2, 9355=1871*5, 9356=2339*2^2, 9357=3119*3, and 9358=4679*2. [Corrected by _Jon E. Schoenfield_, Sep 21 2022]

Cf. A006530, A070087, A079748, A079749 (erroneous version), A100384.

V:= Vector(11): count:= 0:
a:= 1: m:= 1: w:= 1:
for k from 2 while count < 11 do
  v:= max(numtheory:-factorset(k));
  if v > m then m:= v
  else
    if V[k-a] = 0 then V[k-a]:= a; count:= count+1; fi;
    a:= k; m:= v;
  fi
od:
convert(V,list); # Robert Israel, Dec 05 2022

from sympy import factorint
def A358890(n):
    m = 1
    gpf1 = 1
    k = 1
    while 1:
        while 1:
            gpf2 = max(factorint(m+k))
            if gpf2 < gpf1: break
            gpf1 = gpf2
            k += 1
        if k == n: return m
        m += k
        gpf1 = gpf2
        k = 1 # Pontus von Brömssen, Dec 05 2022

A079748(a(n)) = n-1.
From Pontus von Brömssen, Dec 05 2022: (Start)
A079748(a(n)-1) = 0 for n != 3.
For n != 3, a(n) = A070087(m)+1, where m is the smallest positive integer such that A070087(m+1) - A070087(m) = n.
(End)

More terms from Don Reble, Jan 17 2003
Corrected by Jud McCranie, Feb 11 2003
a(14)-a(15) from Giovanni Resta, Jul 25 2013
Name edited, a(1) and a(2) corrected by Pontus von Brömssen, Dec 05 2022
a(16) from Martin Ehrenstein, Dec 07 2022

A079747 Numbers k such that gpf(k-1) < gpf(k) < gpf(k+1), where gpf(k) is the greatest prime factor of k (A006530).

Original entry on oeis.org

2, 9, 10, 21, 22, 25, 28, 33, 46, 57, 58, 78, 82, 85, 91, 92, 93, 106, 115, 121, 126, 133, 136, 141, 145, 148, 166, 169, 170, 171, 172, 176, 177, 178, 190, 201, 205, 213, 217, 221, 222, 226, 232, 235, 236, 248, 253, 261, 262, 276, 289, 290, 301, 316, 325, 346

Offset: 1

Reinhard Zumkeller, Jan 10 2003

nonn

Numbers k such that A079748(k-1) > 1.

			k=25: 25-1 = 24 = 3*2^3, 25 = 5^2 and 25+1 = 26 = 13*2, therefore 25 is a term (3 < 5 < 13).

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A071869, A071870, A082417-A082422.

gpf[n_] := FactorInteger[n][[-1, 1]]; ind = Position[Differences[Array[gpf, 350]], ?(# > 0 &)] // Flatten; ind[[Position[Differences[ind], 1] // Flatten]] + 1 (* _Amiram Eldar, Jun 05 2022 *)

a(n) = A071869(n-1) + 1. - T. D. Noe, Nov 26 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

cp's OEIS Frontend

A358890 a(n) is the first term of the first maximal run of n consecutive numbers with increasing greatest prime factors.

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A079747 Numbers k such that gpf(k-1) < gpf(k) < gpf(k+1), where gpf(k) is the greatest prime factor of k (A006530).

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions