A113692 Semiprimes in A054567.

6, 69, 106, 265, 334, 411, 589, 799, 1041, 1174, 1315, 1959, 2329, 3394, 4659, 5221, 5815, 7099, 8146, 8511, 10869, 16449, 21979, 23181, 23794, 25681, 26326, 31774, 33949, 35439, 36961, 38515, 40101, 43369, 45051, 48511, 50289, 52099, 54874

Offset

1,1

Comments

This sequence, A113692, contains semiprimes from the center straight left along the x-axis in the semiprime spiral of A113688-A113689. A113690 contains semiprimes from the center straight right along the x-axis in the semiprime spiral. A113691 contains semiprimes from the center straight down the y-axis in the semiprime spiral. A113693 contains semiprimes from the center straight up the y-axis in the semiprime spiral.

Links

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

Formula

{a(n)} = Intersection of A001358 and A054567. Semiprimes of the form 4*k^2 - 7*k + 4.

Example

a(4) = 4*9^2 - 7*9 + 4 = 265 = 5 * 53.
a(5) = 4*10^2 - 7*10 + 4 = 334 = 2 * 167.
a(6) = 4*11^2 - 7*11 + 4 = 411 = 3 * 137.
a(4), a(5) and a(6) are horizontally adjacent in the semiprime spiral, hence part of a clump and not isolated semiprimes as in A113688. a(9), a(10) and a(11) are another such horizontal string of 3 adjacent semiprimes.
a(46) = 4*151^2 - 7*151 + 4 = 90151 = 17 * 5303 is the greatest member under 10^5 (it is coincidence that this integer ends, base 10, with the same 151 that is the index of the quadratic).

Mathematica

Select[Table[4*n^2 - 7*n + 4, {n, 200}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)

Prog

(Magma) IsSemiprime:= func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [2..120] | IsSemiprime(s) where s is 4*n^2 - 7*n + 4]; // Vincenzo Librandi, Sep 22 2012

Crossrefs

Cf. A001358, A054567, A113688-A113699.

Sequence in context: A347927 A127184 A333795 * A003362 A197170 A183438

Adjacent sequences: A113689 A113690 A113691 * A113693 A113694 A113695

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 05 2005

Status

approved