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 A076050 Limiting sequence if we start with 2 and successively replace n with 2,3,4,...,n,n+1. 6
 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 2, 3, 4, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS We get 2, 23, 23234, 23234232342345 and so on. The lengths are 1,2,5,14,42,... which are the Catalan numbers: A000108. The sums of the numbers in these strings are also the Catalan numbers. In A071159 the n-digit terms follow the 2, 3, 2, 3, 4, ... rule: the number of terms in which the first n-1 digits are the same is 2, 3, 2, 3, 4, ... and the last digits of the terms are 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, ..., A007001. For example, 1111, 1112, 1121, 1122, 1123, 1211, 1212, 1221, 1222, 1223, 1231, 1232, 1233, 1234. a(A000108(n)) = n+1 and a(m) < n+1 for m < A000108(n). - Reinhard Zumkeller, Feb 17 2012 Let (T(1) < T(2) < ... < T(A000108(m))) denote the sequence of Young tableaux of shape (2^m) ordered lexicographically with respect to their columns, and let f(T(i), T(j)) denote the first label of disagreement among T(i) and T(j). Then, empirically, the reverse of the list (f(T(1), T(2)), f(T(1), T(3)), ..., f(T(1), T(A000108(m)))) agrees with the first A000108(m) - 1 terms in this sequence, for all m > 1, as illustrated in the below example. - John M. Campbell, Sep 07 2018 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 EXAMPLE From John M. Campbell, Sep 07 2018: (Start) There are A000108(3) = 5 Young tableaux of shape (2^3) = (2, 2, 2), which are listed below lexicographically.    [3 6]   [4 6]   [4 6]   [5 6]   [5 6]    [2 5] < [2 5] < [3 5] < [2 4] < [3 4]    [1 4]   [1 3]   [1 2]   [1 3]   [1 2] As above, let (T(1), T(2), ..., T(5)) denote this list. The first label of disagreement between T(1) and T(5) is 2; that between T(1) and T(4) is 3; that between T(1) and T(3) is 2; that between T(1) and T(2) is 3. The sequence (2, 3, 2, 3) agrees with the first 4 terms in this sequence. If we repeat this process using Young tableaux of shape (2^4), we obtain the sequence (2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 4). (End) PROG (PARI) a(n)=local(v, w); if(n<1, 0, v=[1]; while(#v

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Last modified December 15 17:45 EST 2018. Contains 318150 sequences. (Running on oeis4.)