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A105936
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Numbers that are the product of exactly 3 primes and are of the form prime(n) + prime(n+1).
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4
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8, 12, 18, 30, 42, 52, 68, 78, 138, 172, 186, 222, 258, 268, 410, 434, 508, 548, 618, 668, 762, 772, 786, 892, 906, 946, 978, 1002, 1030, 1132, 1334, 1374, 1446, 1542, 1606, 1758, 1866, 1878, 1948, 2006, 2022, 2252, 2334, 2414, 2452, 2468, 2486, 2572, 2588
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OFFSET
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1,1
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COMMENTS
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Minimal triprimes (A014612) of the form prime(n) + prime(n+1).
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LINKS
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FORMULA
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a(n) is equal to the product of 3 primes if the arithmetic mean of prime(n) and prime(n+1) is a semiprime.
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EXAMPLE
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a(2) = 12 because 12 = 5 + 7 = 3*2^2;
a(3) = 18 because 18 = 7 + 11 = 2*3^2.
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MATHEMATICA
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Select[Range[8, 10000, 2], 3 == PrimeOmega[#] && NextPrime[#/2] + NextPrime[#/2, -1] == # &] (* Zak Seidov, Jan 31 2017 *)
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PROG
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(PARI) list(lim)=my(v=List()); forprime(p=2, lim\2, forprime(q=2, min(p, lim\p\2), my(t=2*p*q); if(precprime(p*q)+nextprime(p*q)==t, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017
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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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