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%I #13 Sep 08 2022 08:45:23
%S 4,15,34,249,391,565,771,886,1915,3814,5149,5739,6046,7354,9169,10765,
%T 11611,15814,16321,18429,20665,22426,24259,28141,29499,32311,36769,
%U 39106,43161,48291,52786,53709,57481,60394,63379,65409,67471,69565
%N Semiprimes in A054556.
%C 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.
%H Vincenzo Librandi, <a href="/A113693/b113693.txt">Table of n, a(n) for n = 1..1000</a>
%F {a(n)} = Intersection of A001358 and A054556. Semiprimes of the form 4*k^2 - 9*k + 6.
%e a(27) = 4*97^2 - 9*97 + 6 = 36769 = 83 * 443.
%e a(28) = 4*100^2 - 9*100 + 6 = 39106 = 2 * 19553.
%e a(27) and a(28) are horizontally adjacent in the prime spiral, hence part of a clump and not isolated semiprimes as in A113688.
%e a(45) = 4*157^2 - 9*157 + 6 = 97189 = 17 * 5717 is the greatest member under 10^5.
%t Select[Table[4 n^2 - 9 n + 6, {n, 140}], PrimeOmega[#] == 2 &] (* _Vincenzo Librandi_, Sep 22 2012 *)
%o (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
%Y Cf. A001358, A054556, A113688-A113699.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Nov 05 2005
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