A062721 Numbers k such that k is a product of two primes and k-2 is prime.

4, 9, 15, 21, 25, 33, 39, 49, 55, 69, 85, 91, 111, 115, 129, 133, 141, 159, 169, 183, 201, 213, 235, 253, 259, 265, 295, 309, 319, 339, 355, 361, 381, 391, 403, 411, 445, 451, 469, 481, 489, 493, 501, 505, 511, 543, 559, 565, 573, 579, 589, 633, 649, 655, 679

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 14 2001

Keywords

• nonn
• easy

Comments

This sequence is a subsequence of A107986, which only requires k to be composite. The first term in that sequence which is not in this sequence is 45, a number with three prime factors. - Alonso del Arte, May 03 2014

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000.

Crossrefs

Cf. A006512, A001358, A043326.

Cf. A063637, A046315, A089268.

Programs

Mathematica

Select[ Range[ 2, 1500 ], Plus @@ Last@Transpose@FactorInteger[ # ] == 2 && PrimeQ[ # - 2 ] & ]
Select[Range[700], PrimeOmega[#] == 2 && PrimeQ[# - 2]&] (* Harvey P. Dale, Mar 25 2013 *)

PARI

{ n=0; for (m=1, 10^9, a=prime(m) + 2; f=factor(a)~; if ((length(f)==1 && f[2, 1]==2) || (length(f)==2 && f[2, 1]==1 && f[2, 2]==1), write("b062721.txt", n++, " ", a); if (n==10000, break)) ) } \\ Harry J. Smith, Aug 09 2009