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 A234960 Sequence (or tree) T of primes generated by these rules: 2 is in T; if p is in T, then the greatest prime < 2*p is in T; if p is in T, then the least prime > 2*p is in T; duplicates are deleted as they occur. 3
 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 89, 97, 103, 107, 113, 127, 131, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 199, 211, 223, 227, 251, 257, 263, 271, 277, 281, 293, 307, 313, 317, 331, 337, 347, 353 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The rules generate successive generations g(n) as follows:  g(1) = (2), which begets 3 and 5, so that g(2) = (3,5); then g(3) = (7,11); g(4) = (13,17,19,23); etc.  The number of primes in g(n) is given by A234961, and primes not generated, beginning with 71, are given by A234962.  Conjecture:  the limiting relative density of generated primes is 0. LINKS Clark Kimberling, Table of n, a(n) for n = 1..4000 EXAMPLE Starting with 2, the greatest prime less than 2*2 is 3, and the least prime greater than 2*2 is 5. MATHEMATICA t = NestList[DeleteDuplicates[Flatten[Map[{#, NextPrime[2 #, -1], NextPrime[2 #, 1]} &, #]]] &, {2}, 9]; g = Join[{{2}}, Map[Complement[t[[# + 1]], t[[#]]] &, Range[Length[t] - 1]]] Flatten[g] (* A234960 *) (* Peter J. C. Moses, Dec 30 2013 *) CROSSREFS Cf. A234961 A234962. Sequence in context: A176165 A196230 A233360 * A118850 A322443 A219697 Adjacent sequences:  A234957 A234958 A234959 * A234961 A234962 A234963 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jan 01 2014 STATUS approved

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Last modified June 24 05:09 EDT 2021. Contains 345416 sequences. (Running on oeis4.)