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A090695
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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.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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.
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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.
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CROSSREFS
| Cf. A014574, A091182, A091183.
Sequence in context: A001635 A106172 A189478 * A104074 A140785 A038775
Adjacent sequences: A090692 A090693 A090694 * A090696 A090697 A090698
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KEYWORD
| nonn,fini
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AUTHOR
| William F. Sindelar (w_sindelar(AT)juno.com), Dec 19 2003
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