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A352163 a(n) is the least prime p such that p+3 is divisible by exactly n distinct primes.

%I A352163 #10 Mar 08 2022 11:38:12
%S A352163 2,3,67,907,10007,170167,3233227,74364287,2156564407,79792883167,
%T A352163 2874700358527,106363913265607,4999103923483667,204963260862830467,
%U A352163 15485628496253425507,640920116718070879687,45505328286983032457987,3048856995227863174685327,191219157742953165026391187,14692441860003072638808605267
%N A352163 a(n) is the least prime p such that p+3 is divisible by exactly n distinct primes.
%C A352163 For n>2, a(n) = A002110(n+1)/3-3 if that is prime.  This occurs for n = 3, 5, 6, 7, 8, 9, 14, 16, 46, 47, 70, 101, 113, 168, 175, 200, ...
%e A352163 a(4) = 907 because 907 is prime and 907+3 = 910 = 2*5*7*13 has 4 prime divisors.
%p A352163 f:= proc(p) nops(numtheory:-factorset(p+3)) end proc:
%p A352163 V:= Vector(8): count:= 0:
%p A352163 p:= 1:
%p A352163 while count < 8 do
%p A352163   p:= nextprime(p);
%p A352163   v:= f(p);
%p A352163   if V[v] = 0 then V[v]:= p; count:= count+1; fi
%p A352163 od:
%p A352163 convert(V,list);
%Y A352163 Cf. A002110, A023575.
%K A352163 nonn
%O A352163 1,1
%A A352163 _Robert Israel_, Mar 06 2022
%E A352163 More terms from _David A. Corneth_, Mar 06 2022