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A242330
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Numbers k such that k^2 + 2 is a semiprime.
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7
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2, 6, 7, 11, 12, 17, 18, 27, 29, 35, 37, 42, 43, 48, 51, 53, 54, 55, 60, 65, 66, 69, 72, 73, 75, 79, 83, 84, 87, 90, 93, 97, 115, 119, 125, 132, 133, 135, 137, 141, 144, 150, 153, 155, 159, 161, 165, 169, 174, 183, 186, 187, 189, 191, 192, 195, 198
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OFFSET
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1,1
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COMMENTS
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The semiprimes of this form are: 6, 38, 51, 123, 146, 291, 326, 731, 843, 1227, 1371, 1766, 1851, 2306, 2603, 2811, 2918, 3027, 3602, ....
There are no four consecutive terms in this sequence, that is, a(n) > a(n-3) + 3 (check mod 6). Probably sieve theory can show that this sequence has density 0. - Charles R Greathouse IV, Feb 24 2023
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[300], PrimeOmega[#^2 + 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 [2..200] | IsSemiprime(s) where s is n^2+2];
(PARI) issemi(n)=forprime(p=2, 997, if(n%p==0, return(isprime(n/p)))); bigomega(n)==2
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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