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A356872 a(n) = k is the smallest number such that 3*k+1 contains n distinct prime factors.

%I A356872 #30 Sep 28 2022 11:16:39
%S A356872 1,3,23,303,4363,56723,1077743,33410043,718854803,22284498903,
%T A356872 824526459423,35454637755203,1588862487308763,68321086954276823,
%U A356872 4167586304210886223,213640038906023626563,13032042373267441220363,873146839008918561764343,63739719247651055008797063
%N A356872 a(n) = k is the smallest number such that 3*k+1 contains n distinct prime factors.
%H A356872 David A. Corneth, <a href="/A356872/b356872.txt">Table of n, a(n) for n = 1..349</a>
%F A356872 From _Michael S. Branicky_, Sep 02 2022: (Start)
%F A356872 a(n) >= ceiling((A002110(n)-1)/3).
%F A356872 a(n) <= (c*A002110(n+1)/3-1)/3 for n > 1, and c = 1 or 2 chosen so the expression is an integer, with equality holding for c = 1 for n = 2, 3, 6, 7, ... . (End)
%o A356872 (Python)
%o A356872 from sympy import factorint, isprime
%o A356872 from itertools import count, islice
%o A356872 def f(n): return 1 if isprime(n) else len(factorint(n))
%o A356872 def agen():
%o A356872     n = 1
%o A356872     for k in count(0):
%o A356872         v = f(3*k+1)
%o A356872         while v >= n: yield k; n += 1
%o A356872 print(list(islice(agen(), 7))) # _Michael S. Branicky_, Sep 02 2022
%Y A356872 Cf. A002110, A180278, A219108.
%K A356872 nonn
%O A356872 1,2
%A A356872 _Alex Ratushnyak_, Sep 02 2022
%E A356872 a(8) from _Michael S. Branicky_, Sep 02 2022
%E A356872 a(9)-a(19) from _Jon E. Schoenfield_, Sep 02 2022