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 A229830 Trajectory of 1 under the morphism 1 -> 12, 2 -> 1232, 3 -> 123432, 4 -> 12345432, etc. 1
 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It appears that records occur at A000111. [This is false. - Rémy Sigrist, Nov 15 2018] The n-th local maximum equals a(n) + 1. - Rémy Sigrist, Nov 13 2018 Records at {1, 2, 5, 16, 61, 258, 1161, 5440, 26233, 129282, 648141, 3294864, ...}, which seems to match A104858. - Michael De Vlieger, Nov 13 2018 LINKS Rémy Sigrist, Table of n, a(n) for n = 1..8558 (7 iterations) MATHEMATICA With[{n = 5}, Take[#, LengthWhile[#, # <= n &] + 1] &@ Nest[Flatten[# /. Array[Last@ # - 1 -> Most[#~Join~Reverse@ Most@ #] &@ Range@ # &, Max@ #, 2]] &, {1}, n]] (* Michael De Vlieger, Nov 13 2018 *) PROG (PARI) a = vector(87); a[1]=1; n=0; for (p=1, oo, h=1+a[p]; for (v=1, h, a[n++]=v; print1 (v ", "); if (n==#a, break (2))); forstep (v=h-1, 2, -1, a[n++]=v; print1 (v ", "); if (n==#a, break (2)))) \\ Rémy Sigrist, Nov 13 2018 CROSSREFS Cf. A007001, A000111. Sequence in context: A018194 A338630 A286281 * A105203 A317952 A059131 Adjacent sequences: A229827 A229828 A229829 * A229831 A229832 A229833 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Dec 08 2013 EXTENSIONS Data corrected by Rémy Sigrist, Nov 13 2018 STATUS approved

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Last modified February 6 04:21 EST 2023. Contains 360097 sequences. (Running on oeis4.)