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A113691 Semiprimes in A033951. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

FORMULA

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

EXAMPLE

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.

MATHEMATICA

Select[Table[4*n^2 + 3*n + 1, {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 [1..120] | IsSemiprime(s) where s is 4*n^2 + 3*n + 1]; // Vincenzo Librandi, Sep 22 2012

CROSSREFS

Cf. A001358, A033951, A113688-A113699.

Sequence in context: A085434 A245372 A020351 * A188598 A057454 A260278

Adjacent sequences:  A113688 A113689 A113690 * A113692 A113693 A113694

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 05 2005

STATUS

approved

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Last modified February 24 15:37 EST 2018. Contains 299623 sequences. (Running on oeis4.)