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

2, 3, 67, 907, 10007, 170167, 3233227, 74364287, 2156564407, 79792883167, 2874700358527, 106363913265607, 4999103923483667, 204963260862830467, 15485628496253425507, 640920116718070879687, 45505328286983032457987, 3048856995227863174685327, 191219157742953165026391187, 14692441860003072638808605267

Offset: 1

Author

Robert Israel, Mar 06 2022

Keywords

• nonn

Comments

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, ...

Examples

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

Crossrefs

Cf. A002110, A023575.

Programs

Maple

f:= proc(p) nops(numtheory:-factorset(p+3)) end proc:
V:= Vector(8): count:= 0:
p:= 1:
while count < 8 do
  p:= nextprime(p);
  v:= f(p);
  if V[v] = 0 then V[v]:= p; count:= count+1; fi
od:
convert(V,list);

Extensions

More terms from David A. Corneth, Mar 06 2022