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 A308673 For n > 2, if there exists an m < n such that a(m) = a(n), take the largest such m and set a(n+1) = a(n)+(n-m); otherwise a(n+1) = 1. Start with a(1)=0, a(2)=0. 0
 0, 0, 1, 1, 2, 1, 3, 1, 3, 5, 1, 4, 1, 3, 8, 1, 4, 9, 1, 4, 7, 1, 4, 7, 10, 1, 5, 22, 1, 4, 11, 1, 4, 7, 17, 1, 5, 15, 1, 4, 11, 21, 1, 5, 12, 1, 4, 11, 18, 1, 5, 12, 19, 1, 5, 9, 47, 1, 5, 9, 13, 1, 5, 9, 13, 17, 48, 1, 7, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS It appears that if you choose "otherwise a(n+1) = x" to be a different integer, that the sequence starts to look the same, but offset in position and value. For example, if you compare the case where "otherwise a1(n+1) = 1" and "otherwise a2(n+1) = 2" then a1(n) = a2(n+3)-2. LINKS MATHEMATICA a = a = 0; a[n_] := a[n] = Module[{k = n-2}, While[k > 0 && a[k] != a[n-1], k--]; If[k==0, 1, a[n-1] + n - k - 1]]; Array[a, 100] (* Amiram Eldar, Jul 12 2019 *) PROG (Python) def Prog(length):     L = 2     seq = [0, 0]     while L < length:         x = len(seq)-1         while x > 0:             if seq[-1] == seq[x-1]:                 m = len(seq)-x                 a_n = seq[L-1]                 seq.append(a_n+m)                 x = -1             else:                 x -= 1             if x == 0:                 seq.append(1)         L += 1     return seq CROSSREFS Cf. A181391. Sequence in context: A163313 A337178 A321893 * A324287 A213594 A335105 Adjacent sequences:  A308670 A308671 A308672 * A308674 A308675 A308676 KEYWORD nonn AUTHOR Philip Kalisman, Jul 07 2019 STATUS approved

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Last modified October 27 12:08 EDT 2021. Contains 348276 sequences. (Running on oeis4.)