



86, 298, 371, 1243, 1541, 2426, 2627, 3053, 4258, 5366, 5663, 6281, 6602, 6931, 7613, 8327, 9073, 9458, 10661, 13283, 14702, 15191, 16706, 18293, 18838, 23486, 25361, 26002, 26651, 27973, 28646, 34318, 35063, 36577, 38123, 41311, 43786, 44627
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OFFSET

1,1


COMMENTS

This sequence, A113690, contains semiprimes from the center straight right along the xaxis in the semiprime spiral of A113688A113689. Semiprimes from the center straight left along the xaxis in the semiprime spiral are A113692. A113693 contains semiprimes from the center straight up the yaxis in the semiprime spiral. Semiprimes from the center straight down the yaxis in the semiprime spiral are A113691.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


FORMULA

{a(n)} = Intersection of A001358 and A054552. Semiprimes of the form 4*k^2  3*k + 1.


EXAMPLE

a(10) = 4*37^2  3*37 + 1 = 5366 = 2 * 2683.
a(11) = 4*38^2  3*38 + 1 = 5663 = 7 * 809.
a(10) and a(11) are horizontally adjacent in the prime spiral, hence part of a clump and not isolated semiprimes as in A113688.
a(57) = 4*156^2  3*156 + 1 = 96877 = 11 * 8807 is the greatest member under 10^5.


MATHEMATICA

Select[Table[4*n^2  3*n + 1, {n, 150}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)


PROG

(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


CROSSREFS

Cf. A001358, A054552, A113688A113699.
Sequence in context: A304518 A306112 A184086 * A043379 A256804 A162028
Adjacent sequences: A113687 A113688 A113689 * A113691 A113692 A113693


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Nov 05 2005


EXTENSIONS

Corrected a(6) by Vincenzo Librandi, Sep 22 2012


STATUS

approved



