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A114430
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Primes of the form 1 + product of the first n 3-almost primes A014612.
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0
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97, 32920473601, 1448500838401, 65182537728001, 1491301685600774317670400000001, 48235157779343672198731287466250036763794299837586774072944798728192000000000000000001
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OFFSET
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1,1
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COMMENTS
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3-almost prime analog of primorial primes A005234 (primes p such that 1 + product of primes up to p is prime) as indexed by A014545 (n such that n-th Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime). In that sense, this sequence is indexed by (2, 8, 9, 10, 19, ...).
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LINKS
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FORMULA
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{a(n)} = {1 + Prod[from i = 1 to n] A014612(i)} INTERSECTION {A000040}.
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EXAMPLE
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a(1) = 97 = 96 + 1 = 1 + (8 * 12) = 1 + A014612(1)*A014612(2) = 1 more than the product of the first 2 of the 3-almost primes and is prime.
a(2) = 32920473601 = 1 + (8 * 12 * 18 * 20 * 27 * 28 * 30 * 42) = 1 more than the product of the first 8 of the 3-almost primes and is prime.
a(3) = 1 more than the product of the first 9 of the 3-almost primes and is prime.
a(4) = 1 more than the product of the first 10 of the 3-almost primes and is prime.
a(5) = 1 more than the product of the first 19 of the 3-almost primes and is prime.
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MATHEMATICA
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Select[Rest[FoldList[Times, 1, Select[Range[250], PrimeOmega[#]==3&]]]+1, PrimeQ] (* Harvey P. Dale, Dec 21 2013 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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