A107986 Composite numbers of the form p+2 where p is prime.

4, 9, 15, 21, 25, 33, 39, 45, 49, 55, 63, 69, 75, 81, 85, 91, 99, 105, 111, 115, 129, 133, 141, 153, 159, 165, 169, 175, 183, 195, 201, 213, 225, 231, 235, 243, 253, 259, 265, 273, 279, 285, 295, 309, 315, 319, 333, 339, 351, 355, 361, 369, 375, 381, 385, 391

Offset: 1

Author

Cino Hilliard, Jun 13 2005

Keywords

• easy
• nonn

Comments

This sequence is analogous to the sequence formed by the Goldbach-Euler conjecture that every even number greater than 2 is the sum of 2 primes. If p + 2 is prime then p and p + 2 are twin primes. The number of terms in this sequence is infinite. This follows immediately from the proof that the number of primes p is infinite. Conjecture: The ratio of the number of terms in this sequence to Pi(n) tends to a limit < 1.

The first term in this sequence that is not also in A062721 is 45 = 3^2 * 5. - Alonso del Arte, May 03 2014

Crossrefs

Cf. A062721, A067774, A107987.

Programs

Mathematica

Select[Range[4, 399], Not[PrimeQ[#]] && PrimeQ[# - 2] &] (* Alonso del Arte, May 03 2014 *)

Formula

a(n) = A067774(n) + 2. - Amiram Eldar, Jul 05 2024