A352163 - OEIS

%I #10 Mar 08 2022 11:38:12

%S 2,3,67,907,10007,170167,3233227,74364287,2156564407,79792883167,

%T 2874700358527,106363913265607,4999103923483667,204963260862830467,

%U 15485628496253425507,640920116718070879687,45505328286983032457987,3048856995227863174685327,191219157742953165026391187,14692441860003072638808605267

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

%C 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 a(4) = 907 because 907 is prime and 907+3 = 910 = 2*5*7*13 has 4 prime divisors.

%p f:= proc(p) nops(numtheory:-factorset(p+3)) end proc:

%p V:= Vector(8): count:= 0:

%p p:= 1:

%p while count < 8 do

%p   p:= nextprime(p);

%p   v:= f(p);

%p   if V[v] = 0 then V[v]:= p; count:= count+1; fi

%p od:

%p convert(V,list);

%Y Cf. A002110, A023575.

%K nonn

%O 1,1

%A _Robert Israel_, Mar 06 2022

%E More terms from _David A. Corneth_, Mar 06 2022