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Search: id:A076050
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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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+0
4
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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PROGRAM
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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])
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CROSSREFS
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Cf. A000108, A071159. a(n)=A007001(n)+1.
Sequence in context: A032154 A003051 A097352 this_sequence A130799 A106383 A105500
Adjacent sequences: A076047 A076048 A076049 this_sequence 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 (kristmikl(AT)freemail.hu), Oct 30 2002
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