A113691 Semiprimes in A033951.

46, 77, 218, 1073, 1351, 1502, 1661, 2186, 2998, 4193, 4727, 5006, 5293, 5891, 7183, 8603, 10558, 12266, 13631, 14581, 15563, 19811, 20953, 25202, 27806, 29843, 30538, 31241, 32671, 33398, 35627, 37153, 39502, 40301, 46118, 46981, 49618, 56051

Offset: 1

Author

Jonathan Vos Post, Nov 05 2005

Keywords

• easy
• nonn

Comments

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

Examples

			a(5) = 4*18^2 + 3*18 + 1 = 1351 = 7 * 193.
a(6) = 4*19^2 + 3*19 + 1 = 1502 = 2 * 751.
a(7) = 4*20^2 + 3*20 + 1 = 1661 = 11 * 151.
a(5), a(6) and a(7) are vertically adjacent in the semiprime spiral, hence part of a clump and not isolated semiprimes as in A113688. a(11), a(12) and a(13) are another such vertical string of 3 adjacent semiprimes and so is a(26), a(27) and a(28).
a(52) = 4*152^2 + 3*152 + 1 = 92873 = 11 * 8443 is the greatest member under 10^5.
		

Links

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

Crossrefs

Cf. A001358, A033951, A113688-A113699.

Programs

Magma

IsSemiprime:= func; [s: n in [1..120] | IsSemiprime(s) where s is 4*n^2 + 3*n + 1]; // Vincenzo Librandi, Sep 22 2012

Mathematica

Select[Table[4*n^2 + 3*n + 1, {n, 200}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)

Formula

{a(n)} = Intersection of A001358 and A033951. Semiprimes of the form 4*k^2 + 3*k + 1.