



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
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OFFSET

1,1


COMMENTS

This sequence, A113691, contains semiprimes from the center straight down the yaxis in the semiprime spiral of A113688A113689. A113693 contains semiprimes from the center straight up the yaxis in the semiprime spiral. A113690 contains semiprimes from the center straight right along the xaxis in the semiprime spiral. Semiprimes from the center straight left along the xaxis 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, A113688A113699.
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



