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4, 15, 34, 249, 391, 565, 771, 886, 1915, 3814, 5149, 5739, 6046, 7354, 9169, 10765, 11611, 15814, 16321, 18429, 20665, 22426, 24259, 28141, 29499, 32311, 36769, 39106, 43161, 48291, 52786, 53709, 57481, 60394, 63379, 65409, 67471, 69565
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OFFSET
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1,1
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COMMENTS
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This sequence contains semiprimes from the center straight up the y-axis in the semiprime spiral of A113688-A113689. Semiprimes from the center straight down the y-axis in the semiprime spiral are A113691. Semiprimes from the center straight right along the x-axis in the semiprime spiral are A113690. Semiprimes from the center straight left along the x-axis in the semiprime spiral are A113692.
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LINKS
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FORMULA
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{a(n)} = Intersection of A001358 and A054556. Semiprimes of the form 4*k^2 - 9*k + 6.
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EXAMPLE
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a(27) = 4*97^2 - 9*97 + 6 = 36769 = 83 * 443.
a(28) = 4*100^2 - 9*100 + 6 = 39106 = 2 * 19553.
a(27) and a(28) are horizontally adjacent in the prime spiral, hence part of a clump and not isolated semiprimes as in A113688.
a(45) = 4*157^2 - 9*157 + 6 = 97189 = 17 * 5717 is the greatest member under 10^5.
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MATHEMATICA
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Select[Table[4 n^2 - 9 n + 6, {n, 140}], PrimeOmega[#] == 2 &] (* Vincenzo Librandi, Sep 22 2012 *)
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PROG
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(Magma) IsSemiprime:= func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [2..150] | IsSemiprime(s) where s is 4*n^2 - 9*n + 6]; // Vincenzo Librandi, Sep 22 2012
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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