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A358890
a(n) is the first term of the first maximal run of n consecutive numbers with increasing greatest prime factors.
5
14, 4, 1, 8, 90, 168, 9352, 46189, 2515371, 721970, 6449639, 565062156, 11336460025, 37151747513, 256994754033, 14037913234203
OFFSET
1,1
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
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)
EXAMPLE
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]
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
PROG
(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
CROSSREFS
Cf. A006530, A070087, A079748, A079749 (erroneous version), A100384.
Sequence in context: A182431 A182440 A040187 * A164811 A018813 A070648
KEYWORD
nonn,more
AUTHOR
Reinhard Zumkeller, Jan 10 2003
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
STATUS
approved