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

1,2

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

Links

Table of n, a(n) for n=1..61.

Example

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.

Prog

(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

Crossrefs

Cf. A014574, A091182, A091183.

Sequence in context: A106172 A189478 A364164 * A104074 A140785 A355177

Adjacent sequences: A090692 A090693 A090694 * A090696 A090697 A090698

Keyword

nonn,fini

Author

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

Status

approved