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

Author

Reinhard Zumkeller, Jan 10 2003

Keywords

• nonn
• more

Comments

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

Examples

			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]
		

Crossrefs

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

Programs

Maple

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

Python

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

Formula

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)

Extensions

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