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A114428
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Primes of the form 1 + product of the first n semiprimes.
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OFFSET
| 1,1
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COMMENTS
| Semiprime analogue 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 (1, 4, 5, 6, 11, 12, 39, ...). a(7) added by Jonathan Vos Post jvospost3(AT)gmail.com, Dec 12, 2010.
The next term has 90 digits. [From Harvey P. Dale, Sep 21 2011]
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FORMULA
| {a(n)} = {1 + A112141} INTERSECTION {A000040}.
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EXAMPLE
| a(1) = 5 = 4 + 1 = 1 + A001358(1) = 1 + A112141(1) because 4 is the first semiprime and 5 is prime.
a(2) = 2161 because 2160 + 1 = 1 + A001358(1)*A001358(2)*A001358(3)*A001358(4) = 1 + A112141(4) = 1 + (4*6*9*10) is prime.
a(3) = 1 + A112141(5).
a(4) = 1 + A112141(6).
a(5) = 1 + A112141(11).
a(6) = 1 + A112141(12).
a(7) = (4 * 6 * 9 * 10 * 14 * 15 * 21 * 22 * 25 * 26 * 33 * 34 * 35 * 38 * 39 * 46 * 49 * 51 * 55 * 57 * 58 * 62 * 65 * 69 * 74 * 77 * 82 * 85 * 86 * 87 * 91 * 93 * 94* 95 * 106 * 111 * 115 * 118 * 119) + 1 is prime.
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MATHEMATICA
| Select[#+1&/@FoldList[Times, 1, Select[Range[200], PrimeOmega[#] == 2&]], PrimeQ] (* From Harvey P. Dale, Sep 21 2011 *)
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CROSSREFS
| Cf. A000040, A001358, A002110, A005234, A014545, A112141.
Sequence in context: A024073 A105035 A004816 * A074799 A172942 A067944
Adjacent sequences: A114425 A114426 A114427 * A114429 A114430 A114431
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KEYWORD
| nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 13 2006
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