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A360994
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Numbers k such that (2^k + 1)^3 - 2 is a semiprime.
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3
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0, 1, 2, 4, 5, 6, 13, 14, 18, 27, 43, 45, 63, 76, 85, 108, 115, 119, 123, 187, 211, 215, 283, 312
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OFFSET
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1,3
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COMMENTS
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a(25) >= 355.
623, 674, 711, 766, 767 are also in this sequence, but their position cannot be established before finding any factor for the values corresponding to the following "blockers": 355, 511, 587, 707, 731.
1424, 1470, 1580, 1946, 2117, 2693, 3000, 3540, 4164, 7043, 9475, 10632, 15018, 19064, 27130, 28266, 28532, 46434, 58768, 103536 are some larger members of this sequence, but their position cannot be established. These produce "trivial" semiprimes where one prime is small (e.g., 3 or 5).
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[70], PrimeOmega[(2^# + 1)^3 - 2] == 2 &]
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PROG
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(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..70]| IsSemiprime(s) where s is (2^n+1)^3-2];
(PARI) isok(n) = bigomega((2^n+1)^3-2) == 2;
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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