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%I #8 Sep 08 2022 08:45:23
%S 86,298,371,1243,1541,2426,2627,3053,4258,5366,5663,6281,6602,6931,
%T 7613,8327,9073,9458,10661,13283,14702,15191,16706,18293,18838,23486,
%U 25361,26002,26651,27973,28646,34318,35063,36577,38123,41311,43786,44627
%N Semiprimes in A054552.
%C This sequence, A113690, contains semiprimes from the center straight right along the x-axis in the semiprime spiral of A113688-A113689. Semiprimes from the center straight left along the x-axis in the semiprime spiral are A113692. A113693 contains semiprimes from the center straight up the y-axis in the semiprime spiral. Semiprimes from the center straight down the y-axis in the semiprime spiral are A113691.
%H Vincenzo Librandi, <a href="/A113690/b113690.txt">Table of n, a(n) for n = 1..1000</a>
%F {a(n)} = Intersection of A001358 and A054552. Semiprimes of the form 4*k^2 - 3*k + 1.
%e a(10) = 4*37^2 - 3*37 + 1 = 5366 = 2 * 2683.
%e a(11) = 4*38^2 - 3*38 + 1 = 5663 = 7 * 809.
%e a(10) and a(11) are horizontally adjacent in the prime spiral, hence part of a clump and not isolated semiprimes as in A113688.
%e a(57) = 4*156^2 - 3*156 + 1 = 96877 = 11 * 8807 is the greatest member under 10^5.
%t Select[Table[4*n^2 - 3*n + 1, {n, 150}], PrimeOmega[#] == 2&] (* _Vincenzo Librandi_, Sep 22 2012 *)
%o (Magma) IsSemiprime:= func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [1..120] | IsSemiprime(s) where s is 4*n^2 - 3*n + 1]; // _Vincenzo Librandi_, Sep 22 2012
%Y Cf. A001358, A054552, A113688-A113699.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Nov 05 2005
%E Corrected a(6) by _Vincenzo Librandi_, Sep 22 2012
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