A090695 Integers which are not the sum of 2 integers A and B with AB+1 and AB-1 both primes. In other words, the product cannot be the middle integer of a Twin Prime pair.

1, 2, 3, 6, 10, 12, 14, 15, 20, 26, 30, 40, 45, 54, 60, 66, 75, 80, 90, 100, 105, 117, 120, 150, 180, 250, 270, 280, 290, 315, 320, 342, 360, 390, 410, 432, 440, 450, 455, 480, 495, 510, 540, 560, 590, 630, 645, 765, 810, 980, 1080, 1170, 1220, 1305, 1430, 1530, 1860, 2235, 2310, 2670, 3120

Offset: 1

Author

William F. Sindelar (w_sindelar(AT)juno.com), Dec 19 2003

Keywords

• nonn
• fini

Comments

Sequence may be finite. Next term after 3120 if it exists must be greater than 867750.

If the sequence can be proved to be finite, then one may surmise that there are infinitely many twin primes and that every integer greater than 3120 and every prime, except 2 and 3, is the sum of 2 integers whose product is the middle number of a twin prime pair.

If there is a term after 3120, it is larger than 4*10^9. - Giovanni Resta, Oct 31 2017

Examples

			15 is a member: 15 is the sum of these pairs of integers: (2+13) (3+12) (4+11) (5+10) (6+9) (7+8). Their products (2*13) (3*12), etc. plus and minus 1 are not primes and therefore the products cannot be the middle integers of Twin Prime sets.
		

Crossrefs

Cf. A014574, A091182, A091183.

Programs

PARI

isok(n) = {for (a=1, n\2, ab = a*(n-a); if (isprime(ab+1) && isprime(ab-1), return (0));); return (1);} \\ Michel Marcus, Jul 12 2013