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A076050
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Limiting sequence if we start with 2 and successively replace n by 2,3,4,...n,n+1.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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]
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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PROG
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(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])
(Haskell)
a076050 n = a076050_list !! (n-1)
a076050_list = 2 : f [2] where
f xs = (drop (length xs) xs') ++ (f xs') where
xs' = concatMap ((enumFromTo 2) . (+ 1)) xs
-- Reinhard Zumkeller, Feb 17 2012
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CROSSREFS
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Cf. A000108, A071159. a(n)=A007001(n)+1.
Sequence in context: A257396 A237582 A097352 * A130799 A243519 A106383
Adjacent sequences: A076047 A076048 A076049 * A076051 A076052 A076053
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Miklos Kristof, Oct 30 2002
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STATUS
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approved
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