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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.

%I A358890 #31 Dec 10 2022 23:35:27
%S A358890 14,4,1,8,90,168,9352,46189,2515371,721970,6449639,565062156,
%T A358890 11336460025,37151747513,256994754033,14037913234203
%N A358890 a(n) is the first term of the first maximal run of n consecutive numbers with increasing greatest prime factors.
%C A358890 a(16) > 10^13. - _Giovanni Resta_, Jul 25 2013
%C A358890 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
%C A358890 a(17) > 10^14. - _Martin Ehrenstein_, Dec 10 2022
%F A358890 A079748(a(n)) = n-1.
%F A358890 From _Pontus von Brömssen_, Dec 05 2022: (Start)
%F A358890 A079748(a(n)-1) = 0 for n != 3.
%F A358890 For n != 3, a(n) = A070087(m)+1, where m is the smallest positive integer such that A070087(m+1) - A070087(m) = n.
%F A358890 (End)
%e A358890 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]
%p A358890 V:= Vector(11): count:= 0:
%p A358890 a:= 1: m:= 1: w:= 1:
%p A358890 for k from 2 while count < 11 do
%p A358890   v:= max(numtheory:-factorset(k));
%p A358890   if v > m then m:= v
%p A358890   else
%p A358890     if V[k-a] = 0 then V[k-a]:= a; count:= count+1; fi;
%p A358890     a:= k; m:= v;
%p A358890   fi
%p A358890 od:
%p A358890 convert(V,list); # _Robert Israel_, Dec 05 2022
%o A358890 (Python)
%o A358890 from sympy import factorint
%o A358890 def A358890(n):
%o A358890     m = 1
%o A358890     gpf1 = 1
%o A358890     k = 1
%o A358890     while 1:
%o A358890         while 1:
%o A358890             gpf2 = max(factorint(m+k))
%o A358890             if gpf2 < gpf1: break
%o A358890             gpf1 = gpf2
%o A358890             k += 1
%o A358890         if k == n: return m
%o A358890         m += k
%o A358890         gpf1 = gpf2
%o A358890         k = 1 # _Pontus von Brömssen_, Dec 05 2022
%Y A358890 Cf. A006530, A070087, A079748, A079749 (erroneous version), A100384.
%K A358890 nonn,more
%O A358890 1,1
%A A358890 _Reinhard Zumkeller_, Jan 10 2003
%E A358890 More terms from _Don Reble_, Jan 17 2003
%E A358890 Corrected by _Jud McCranie_, Feb 11 2003
%E A358890 a(14)-a(15) from _Giovanni Resta_, Jul 25 2013
%E A358890 Name edited, a(1) and a(2) corrected by _Pontus von Brömssen_, Dec 05 2022
%E A358890 a(16) from _Martin Ehrenstein_, Dec 07 2022