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Search: id:A111170
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| A111170 |
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Semiprimes S such that 3*S + 1 is also a semiprime. |
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+0
6
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| 15, 35, 38, 39, 55, 62, 82, 86, 87, 91, 106, 111, 115, 118, 119, 134, 142, 155, 159, 178, 187, 194, 218, 226, 235, 254, 259, 267, 278, 287, 295, 298, 299, 314, 319, 326, 327, 334, 335, 339, 371, 382, 386, 391, 395, 398, 411, 422, 427, 446, 451, 454, 502, 515
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is analogous to Sophie Germain semiprimes A111153 and the chains shown are analogous to Cunningham chains of the first kind and Tomaszewski chains of the first 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: 111, 334, 1003; 142, 427, 1282. Length 4: 35, 106, 319, 958; 86, 259, 778, 2335; 187, 562, 1687, 5062.
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FORMULA
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{a(n)} = a(n) is an element of A001358 and 3*a(n)+1 is an element of A001358.
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EXAMPLE
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n s(n) 3*s + 1
1 15 = 3 * 5 46 = 2 * 23
2 35 = 5 * 7 106 = 2 * 53
3 38 = 2 * 19 115 = 5 * 23
4 39 = 3 * 13 118 = 2 * 59
5 55 = 5 * 11 166 = 2 * 83
6 62 = 2 * 31 187 = 11 * 17
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CROSSREFS
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Cf. A001358, A111153, A111168, A111171, A111173, A111176.
Sequence in context: A139578 A156662 A027443 this_sequence A134335 A080774 A146319
Adjacent sequences: A111167 A111168 A111169 this_sequence A111171 A111172 A111173
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 22 2005
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