A080899 Primes p(k) such that every composite number between p(k) and p(k+1) has exactly three distinct prime factors.

29, 41, 59, 101, 137, 149, 179, 197, 227, 239, 269, 281, 311, 347, 521, 599, 617, 641, 643, 739, 809, 821, 827, 881, 1031, 1061, 1277, 1451, 1487, 1579, 1607, 1619, 1667, 1697, 1787, 1871, 1877, 1997, 2027, 2081, 2087, 2111, 2237, 2267, 2293, 2381

Offset: 1

Author

Ralf Stephan, Mar 30 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

See A075583 for another version.

Programs

Mathematica

Select[Partition[Prime[Range[2, 360]], 2, 1], AllTrue[Range[First[#]+1, Last[#]-1], PrimeNu[#1] == 3 &] &][[;;,1]] (* Amiram Eldar, Sep 14 2024 *)

PARI

forprime(p=3, 3000, f=0; for(k=p+1, nextprime(p+1)-1, if(omega(k)!=3, f=1; break)); if(!f, print1(p", ")))