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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

Table of n, a(n) for n=1..70.

MATHEMATICA

a[1] = a[2] = 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.)