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A242244
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Primes p such that both p^2 + 2 and p^2 - 2 are semiprimes.
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2
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11, 17, 53, 73, 79, 83, 97, 251, 269, 281, 379, 389, 433, 461, 601, 631, 691, 739, 827, 929, 947, 983, 1033, 1087, 1187, 1303, 1423, 1483, 1531, 1637, 1709, 1847, 1879, 2447, 2473, 2683, 2833, 2843, 3301, 3463, 3557, 3719, 3727, 3779, 3833, 3907, 3931, 4157
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OFFSET
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1,1
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COMMENTS
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Primes p such that p^2 + 2 = 3q, where q is prime, and p^2 - 2 is semiprime.
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LINKS
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EXAMPLE
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a(1) = 11 is prime: 11^2 + 2 = 123 = 3 * 41 which is semiprime: 11^2 - 2 = 119 = 7 * 17 which is also semiprime.
a(2) = 17 is prime: 17^2 + 2 = 291 = 3 * 97 which is semiprime: 17^2 - 2 = 287 = 7 * 41 which is also semiprime.
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MAPLE
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with(numtheory):A242244:= proc()if isprime(x) and bigomega(x^2+2)=2 and bigomega(x^2-2)=2 then RETURN (x); fi; end: seq(A242244 (), x=1..5000);
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MATHEMATICA
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A242244 = {}; Do[p = Prime[n]; If[PrimeOmega[p^2 + 2] == 2 && PrimeOmega[p^2 - 2] == 2, AppendTo[A242244, p]], {n, 2000}]; A242244
Select[Prime[Range[600]], PrimeOmega[#^2+{2, -2}]=={2, 2}&] (* Harvey P. Dale, Apr 07 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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