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A136353
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First odd composite N divisible by precisely the first n odd primes with N-2 prime.
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3
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9, 15, 105, 1155, 15015, 255255, 4849845, 111546435, 9704539845, 100280245065, 18551845337025, 152125131763605, 98120709987525225, 7071232499767651215, 16294579238595022365, 33648306127698721183725, 527797716117331369424715
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OFFSET
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1,1
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COMMENTS
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This sequence is different from A070826 and A118750.
Contribution from Enoch Haga, Jul 02 2009: (Start)
A clearer definition of the sequence: a(n) is the smallest odd composite
number m such that m - 2 is prime and set of the distinct prime factors of m
equals the set of the first n odd primes. Farideh Firoozbakthkt, Jun 30, 2009
(End)
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n=1..200
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FORMULA
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Compute N = product of the first n odd primes. If N-2 is prime, add N to the sequence. Otherwise test 3N, 5N, 7N, 9N, ... until kN - 2 is prime, subject to A006530(k) <= n+1.
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EXAMPLE
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The first odd prime is 3. 3-1 is not prime, but 3*3-2 = 7 is prime so a(1) = 9. The product of the first two odd primes is 15, and 15-2 is prime, so a(2) = 15.
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MATHEMATICA
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a[n_]:=(c=Product[Prime[k], {k, 2, n+1}]; For[m=1, !(!PrimeQ[c (2m-1)]&&PrimeQ[c(2m-1)-2]&&Length[FactorInteger[c(2m-1)]]==n), m++ ]; c(2m-1)); Table[a[n], {n, 20}] [From Enoch Haga, Jul 02 2009]
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CROSSREFS
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Cf. A136349-A136352 A136354-A136358 A070826 A118750.
Sequence in context: A152219 A173037 A029712 * A136354 A177184 A098146
Adjacent sequences: A136350 A136351 A136352 * A136354 A136355 A136356
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KEYWORD
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nonn,changed
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AUTHOR
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Enoch Haga, Dec 25 2007
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EXTENSIONS
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More terms, better title, and Mathematica program from Farideh Firoozbakht received Jun 30, 2009. - Enoch Haga, Jul 02 2009
Further editing by Charles R Greathouse IV, Oct 05 2009
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STATUS
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approved
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