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A059324
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Numbers n such that 6n+5 is composite.
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4
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5, 10, 12, 15, 19, 20, 23, 25, 26, 30, 33, 34, 35, 36, 40, 45, 47, 49, 50, 53, 54, 55, 56, 60, 61, 62, 65, 67, 68, 70, 72, 75, 78, 80, 82, 85, 87, 88, 89, 90, 91, 95, 96, 100, 101, 103, 104, 105, 110, 111, 114, 115, 117, 118, 120, 121, 122, 124, 125, 127, 129, 130
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture : There exists no pair of primes (p,q>p^2) such that q-p^2 = 6*n-4 (see A138479) - Philippe LALLOUET (philip.lallouet(AT)orange.fr), Mar 20 2008
Let p=prime number, n=(p^2+2p-5)/6 mod (p); ex: 10=(5^2+10-5)/6 mod (5); 34 = (11^2+22-5)/6 mod (11); or n=(p^2+4p-5)/6 mod (p); ex: 19=(7^2+28-5)/6 mod (7). [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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FORMULA
| a(n) = A046953(n-1)-1
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EXAMPLE
| a(3)=12 because 6*12+5=77 is composite.
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MATHEMATICA
| Select[Range[200], !PrimeQ[6#+5]&] (* From Harvey P. Dale, Mar 13 2011 *)
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CROSSREFS
| Complement of A059325.
Cf. A138479.
Sequence in context: A033649 A050680 A162821 * A112776 A120063 A101839
Adjacent sequences: A059321 A059322 A059323 * A059325 A059326 A059327
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KEYWORD
| nonn,easy
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AUTHOR
| A. Joha (A.S.J.R.Joha(AT)student.tbm.tudelft.nl), Jan 26 2001
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EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), Jan 29 2001
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