OFFSET
1,1
COMMENTS
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.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
EXAMPLE
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.
MATHEMATICA
Select[Table[4 n^2 - 9 n + 6, {n, 140}], PrimeOmega[#] == 2 &] (* Vincenzo Librandi, Sep 22 2012 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Nov 05 2005
STATUS
approved