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 A136353 First odd composite N divisible by precisely the first n odd primes with N-2 prime. 3
 9, 15, 105, 1155, 15015, 255255, 4849845, 111546435, 9704539845, 100280245065, 18551845337025, 152125131763605, 98120709987525225, 7071232499767651215, 16294579238595022365, 33648306127698721183725, 527797716117331369424715 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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) LINKS Charles R Greathouse IV, Table of n, a(n) for n=1..200 FORMULA 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. EXAMPLE 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. MATHEMATICA 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] CROSSREFS Sequence in context: A152219 A173037 A029712 * A136354 A177184 A098146 Adjacent sequences:  A136350 A136351 A136352 * A136354 A136355 A136356 KEYWORD nonn,changed AUTHOR Enoch Haga, Dec 25 2007 EXTENSIONS 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 STATUS approved

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