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 A179921 a(n) = prime(n) if n<=3; for n>3, a(n) is the smallest prime >a(n-1), such that the denominator of fraction (a(n-1)-a(n-2))/(a(n)-a(n-1)) did not appear earlier. 0
 2, 3, 5, 7, 13, 23, 31, 53, 67, 79, 113, 131, 151, 193, 233, 271, 307, 353, 379, 409, 457, 557, 613, 691, 761, 809, 883, 907, 1013, 1069, 1123, 1181, 1213, 1279, 1361, 1423, 1483, 1571, 1657, 1709, 1811, 1933, 1997, 2087, 2179, 2273, 2341, 2459 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Using Dirichlet's theorem on arithmetic progressions, it is easy to prove that the sequence is infinite.  The sequence of the corresponding denominators begins with 2,1,3,5,4,11,7,6,17, ... LINKS EXAMPLE The first four terms 2,3,5,13 give three denominators: 2,1,3. Then a(5) is not in {17, 19}, since (13-5)/(17-13) = 2/1, (13-5)/(19-13) = 4/3 and denominators 1 and 3 already appeared earlier. Since (13-5)/(23-13) = 4/5 and 5 is not yet in the denominator sequence, a(5) = 23. CROSSREFS Cf. A168253, A178942, A179210, A179234, A179256, A179328. Sequence in context: A163487 A048413 A064336 * A211073 A182315 A233862 Adjacent sequences:  A179918 A179919 A179920 * A179922 A179923 A179924 KEYWORD nonn AUTHOR Vladimir Shevelev, Jan 12 2011 EXTENSIONS Edited by Alois P. Heinz, Jan 12 2011 STATUS approved

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Last modified May 19 20:41 EDT 2019. Contains 323410 sequences. (Running on oeis4.)