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A111171
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Semiprimes S such that 3*S - 1 is also a semiprime.
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5
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9, 21, 22, 25, 26, 49, 62, 65, 69, 74, 85, 93, 121, 122, 129, 133, 141, 146, 158, 161, 166, 178, 185, 194, 205, 209, 221, 249, 253, 262, 265, 289, 298, 302, 305, 309, 346, 358, 361, 365, 381, 382, 386, 413, 446, 466, 473, 485, 489, 493, 501, 505, 514, 526, 553
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is analogous to Sophie Germain semiprimes A111153 and the chains shown are analogous to Cunningham chains of the second kind and Tomaszewski chains of the second kind. Define a 3n-1 semiprime chain of length k. This is a sequence of semiprimes s(1) < s(2) < ... < s(k) such that s(i+1) = 3*s(i) - 1 for i = 1, ..., k-1. Length 3: 9, 26, 77; 49, 146, 437; 65, 194, 581; 129, 386, 1157; 158, 473, 1418; 187, 562, 1685. Length 4: 74, 221, 662, 1985; 122, 365, 1094, 3281. Length 5: 21, 62, 185, 554, 1661.
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FORMULA
| {a(n)} = a(n) is an element of A001358 and 3*a(n)-1 is an element of A001358.
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EXAMPLE
| n s(n) 3 *s -1
1 9 = 3^2 26 = 2 * 13
2 21 = 3 * 7 62 = 2 * 31
3 22 = 2 * 11 65 = 5 * 13
4 25 = 5^2 74 = 2 * 37
5 26 = 2 * 13 77 = 7 * 11
6 49 = 7^2 146 = 2 * 73
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CROSSREFS
| Cf. A001358, A111153, A111168, A111170, A111173, A111176.
Sequence in context: A143243 A157812 A161326 * A067887 A174870 A141603
Adjacent sequences: A111168 A111169 A111170 * A111172 A111173 A111174
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2005
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EXTENSIONS
| Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 22 2005
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