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A241659
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Primes p such that p^3 + 2 is semiprime.
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3
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2, 11, 13, 17, 19, 23, 31, 41, 53, 59, 89, 101, 131, 137, 149, 193, 211, 223, 227, 229, 233, 239, 251, 271, 293, 317, 331, 359, 401, 449, 461, 557, 563, 571, 593, 599, 619, 641, 659, 677, 691, 719, 739, 751, 809, 821, 853, 929, 971, 991, 1009, 1013, 1039, 1051
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OFFSET
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1,1
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LINKS
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EXAMPLE
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11 is prime and appears in the sequence because 11^3 + 2 = 1333 = 31 * 43, which is a semiprime.
17 is prime and appears in the sequence because 17^3 + 2 = 4915 = 5 * 983, which is a semiprime.
37 is prime but does not appear in the sequence because 37^3 + 2 = 50655 = 3 * 5 * 11 * 983, which is not a semiprime.
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MAPLE
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with(numtheory): KD:= proc() local a, b, k; k:=ithprime(n); a:=bigomega(k^3+2); if a=2 then RETURN (k); fi; end: seq(KD(), n=1..500);
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MATHEMATICA
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(*For the b-file*) c = 0; Do[t = Prime[n]; If[PrimeOmega[t^3 + 2] == 2, c++; Print[c, " ", t]], {n, 1, 6*10^4}];
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PROG
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(PARI) s=[]; forprime(p=2, 1200, if(bigomega(p^3+2)==2, s=concat(s, p))); s \\ Colin Barker, Apr 27 2014
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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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