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A113432
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Pierpont semiprimes: semiprimes of the form (2^K)*(3^L)+1.
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9
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4, 9, 10, 25, 33, 49, 55, 65, 82, 129, 145, 217, 289, 649, 865, 973, 1537, 1945, 2049, 2305, 3073, 4097, 4609, 5833, 6145, 6913, 8193, 8749, 9217, 11665, 13123, 15553, 20737, 23329, 24577, 27649, 31105, 34993, 41473, 62209, 69985, 73729, 78733
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Caldwell, C., "Pierpont primes." primeform posting, Oct 25, 2005.
Eric Weisstein's World of Mathematics, Pierpont Prime
Eric Weisstein's World of Mathematics, Semiprime
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FORMULA
| {a(n)} = Intersection of {(2^K)*(3^L)+1} A055600 and semiprimes A001358. a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 2.
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EXAMPLE
| a(1) = 4 = (2^0)*(3^1)+1 = 2^2 hence the semiprime A001358(1).
a(2) = 9 = (2^3)*(3^0)+1 = 3^2 hence the semiprime A001358(3).
a(3) = 10 = (2^0)*(3^2)+1 = 2 * 5 hence the semiprime A001358(4).
a(4) = 25 = (2^3)*(3^1)+1 = 5^2 hence the semiprime A001358(9).
a(5) = 33 = (2^5)*(3^0)+1 = 3 * 11 hence the semiprime A001358(11).
a(6) = 49 = (2^4)*(3^1)+1 = 7^2 hence the semiprime A001358(17).
a(7) = 55 = (2^1)*(3^3)+1 = 5 * 11 hence the semiprime A001358(19).
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MATHEMATICA
| Select[Range[10^5], Plus @@ Last /@ FactorInteger[ # ] == 2 && Max @@ First /@ FactorInteger[ # - 1] < 5 &] (*Chandler*)
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CROSSREFS
| Cf. A001358, A003586, A005109, A055600, A111153, A111206, A113433, A113434.
Sequence in context: A077584 A093896 A191905 * A129830 A113434 A141395
Adjacent sequences: A113429 A113430 A113431 * A113433 A113434 A113435
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 01 2005
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