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A263990
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Nonsquare numbers k such that k and k+1 are semiprimes.
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7
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14, 21, 33, 34, 38, 57, 85, 86, 93, 94, 118, 122, 133, 141, 142, 145, 158, 177, 201, 202, 205, 213, 214, 217, 218, 253, 298, 301, 302, 326, 334, 381, 393, 394, 445, 446, 453, 481, 501, 514, 526, 537, 542, 553, 565, 622, 633, 634, 694, 697, 698, 706, 717, 745, 766, 778, 793, 802, 817, 842, 865, 878
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OFFSET
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1,1
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COMMENTS
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If k and k+1 are semiprimes then k+1 is always nonsquare while k can be a square (see A263951). The sequence gives the nonsquare terms of A070552. Each of the numbers k and k+1 is a product of two distinct primes.
The subsequence of triples of consecutive squarefree semiprimes is A039833. - R. J. Mathar, Aug 13 2019
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LINKS
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MATHEMATICA
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Select[Range[1000], ! IntegerQ[Sqrt[#]] && 2 == PrimeOmega[#] == PrimeOmega[# + 1] &]
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PROG
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(PARI) is(n)=if(n%2, isprime((n+1)/2) && bigomega(n)==2 && !isprimepower(n), isprime(n/2) && bigomega(n+1)==2) \\ Charles R Greathouse IV, Apr 25 2016
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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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