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 A111170 Semiprimes S such that 3*S + 1 is also a semiprime. 5
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS FORMULA {a(n)} = a(n) is an element of A001358 and 3*a(n)+1 is an element of A001358. EXAMPLE 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 CROSSREFS Cf. A001358, A111153, A111168, A111171, A111173, A111176. Sequence in context: A205148 A253055 A338063 * A134335 A257591 A284406 Adjacent sequences:  A111167 A111168 A111169 * A111171 A111172 A111173 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Oct 21 2005 EXTENSIONS Extended by Ray Chandler, Oct 22 2005 STATUS approved

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Last modified January 24 21:49 EST 2022. Contains 350565 sequences. (Running on oeis4.)