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A076050 Limiting sequence if we start with 2 and successively replace n with 2,3,4,...,n,n+1. 6

%I

%S 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,

%T 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,

%U 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

%N Limiting sequence if we start with 2 and successively replace n with 2,3,4,...,n,n+1.

%C 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.

%C 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.

%C a(A000108(n)) = n+1 and a(m) < n+1 for m < A000108(n). [_Reinhard Zumkeller_, Feb 17 2012]

%H Reinhard Zumkeller, <a href="/A076050/b076050.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) a(n)=local(v,w); if(n<1,0,v=[1]; while(#v<n,w=[]; for(i=1,#v,w=concat(w,vector(v[i]+1,j,j))); v=w); 1+v[n])

%o (Haskell)

%o a076050 n = a076050_list !! (n-1)

%o a076050_list = 2 : f [2] where

%o f xs = (drop (length xs) xs') ++ (f xs') where

%o xs' = concatMap ((enumFromTo 2) . (+ 1)) xs

%o -- _Reinhard Zumkeller_, Feb 17 2012

%Y Cf. A000108, A071159. a(n)=A007001(n)+1.

%K easy,nonn,nice

%O 1,1

%A _Miklos Kristof_, Oct 30 2002

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Last modified February 20 02:47 EST 2018. Contains 299357 sequences. (Running on oeis4.)