A075583 Primes p such that the composite numbers between p and the next prime together contain exactly three distinct prime factors.

7, 29, 41, 59, 101, 137, 149, 179, 197, 227, 239, 269, 281, 311, 347, 521, 599, 617, 641, 809, 821, 827, 881, 1031, 1061, 1277, 1451, 1487, 1607, 1619, 1667, 1697, 1787, 1871, 1877, 1997, 2027, 2081, 2087, 2111, 2237, 2267, 2381, 2657, 2687, 2711, 2801, 2999

Offset

1,1

Comments

p+2 is prime for all members p except 7. - David Wasserman, Jan 20 2005

Links

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

Prog

(Magma) a:=[]; for k in PrimesInInterval(2, 3000) do b:={}; for s in [k..NextPrime(k)-1] do if not IsPrime(s) then b:=b join Set(PrimeDivisors(s)); end if; end for; if #Set(b) eq 3 then  Append(~a, k); end if; end for; a; // Marius A. Burtea, Sep 26 2019

Crossrefs

Cf. A052297, A075580, A059960, A075584, A075585, A075586, A075587, A075588, A075589.

See A080899 for another version.

Sequence in context: A156124 A155476 A166970 * A103603 A045465 A330723

Adjacent sequences: A075580 A075581 A075582 * A075584 A075585 A075586

Keyword

nonn

Author

Amarnath Murthy, Sep 26 2002

Extensions

More terms from David Wasserman, Jan 20 2005

Status

approved