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A375390
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Numbers k such that k^2 + 1, k^2 + 3 and k^2 + 5 are semiprimes.
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2
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44, 102, 104, 108, 152, 188, 226, 234, 296, 328, 426, 526, 586, 692, 720, 842, 846, 856, 926, 994, 1076, 1278, 1284, 1386, 1426, 1484, 1498, 1574, 1704, 1746, 1764, 1822, 1826, 1848, 1952, 2058, 2114, 2128, 2142, 2148, 2164, 2186, 2386, 2416, 2442, 2484, 2640, 2704, 2904, 2948, 3108, 3142, 3164
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OFFSET
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1,1
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COMMENTS
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All terms are even.
a(n)^2 + 3 or a(n)^2 + 5 is 3 times a prime. In the first case, a(n)/3 is in A111051.
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LINKS
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EXAMPLE
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a(3) = 104 is a term because 104^2 + 1 = 10817 = 29 * 373, 104^2 + 3 = 10819 = 31 * 349 and 104^2 + 5 = 10821 = 3 * 3607 are all semiprimes.
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MAPLE
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select(t -> andmap(s -> numtheory:-bigomega(t^2+s)=2, [1, 3, 5]), 2*[$1..2000]);
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MATHEMATICA
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Select[Range[3000], 2 == PrimeOmega[1 + #^2] == PrimeOmega[3 +
#^2] == PrimeOmega [5 + #^2] &]
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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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