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86, 298, 371, 1243, 1541, 2462, 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; internal format)
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OFFSET
| 1,1
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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.
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FORMULA
| {a(n)} = Intersection of A001358 and A054552. Semiprimes of the form 4*k^2 - 3*k + 1.
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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.
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CROSSREFS
| Cf. A001358, A054552, A113688-A113699.
Sequence in context: A097693 A184087 A184086 * A043379 A162028 A157443
Adjacent sequences: A113687 A113688 A113689 * A113691 A113692 A113693
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 05 2005
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