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A113690 Semiprimes in A054552. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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, A113688-A113699.

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

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Last modified October 21 19:08 EDT 2018. Contains 316427 sequences. (Running on oeis4.)