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A372582
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Numbers k such that 2*k + 3 and 3*k + 2 are semiprimes.
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1
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11, 24, 31, 44, 69, 71, 92, 99, 100, 101, 107, 108, 109, 123, 125, 128, 131, 132, 148, 160, 181, 184, 204, 207, 224, 235, 243, 245, 249, 251, 263, 267, 271, 288, 289, 297, 304, 332, 347, 348, 355, 357, 359, 360, 364, 371, 373, 380, 384, 389, 400, 420, 423, 445, 448, 449, 451, 459, 460, 465, 485
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OFFSET
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1,1
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COMMENTS
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The first k where k, k + 1 and k + 2 are all terms is 99. There is no k where k, k + 1, k + 2 and k + 3 are all terms, because 3 * t + 2 is divisible by 4 for t = one of these.
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LINKS
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EXAMPLE
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a(3) = 31 is a term because 2 * 31 + 3 = 65 = 5 * 13 and 3 * 31 + 2 = 95 = 5 * 19 are both semiprimes.
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MAPLE
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filter:= k -> numtheory:-bigomega(3*k+2) = 2 and numtheory:-bigomega(2*k+3) = 2:
select(filter, [$1..1000]);
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MATHEMATICA
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s = {}; Do[If[2 == PrimeOmega[2*k + 3] == PrimeOmega[3*k + 2], AppendTo[s, k]], {k, 10^3}]; s
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CROSSREFS
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KEYWORD
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nonn,new
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AUTHOR
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STATUS
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approved
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