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A062406
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a(n) = cardinality of the (ordered) list L_n defined inductively by: L_1 = {2}; L_(n+1) = L_n - {p}, where p is the first member of L_n, from left to right, such that Prime(n+1) can be appended to the end or beginning of p so that the neighboring digits are equal, if p exists; = L_n + {Prime(n+1)} (append Prime(n+1) to the end of L_n), otherwise.
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1
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1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 5, 6, 5, 6, 7, 8, 7, 6, 5, 6, 7, 8, 7, 6, 5, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| It appears that a(n) is growing slowly on the average. (A moving average filter applied to the sequence will show an upward trend.) Probably a(n) > 0 for all n, but lacking a proof, one is never sure. For example, L_8 = {5} comes perilously close to extinction. It would be interesting to have a closed-form expression giving, at least asymptotically, the value of a(n).
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EXAMPLE
| L_n for n = 1,...,5 are: {2}, {2,3}, {2,3,5}, {2,3,5,7}, {2,3,5,7,11}. The first five values of the sequence are then 1,2,3,4,5, respectively. For n = 6, Prime(6) = 13 can be appended to the beginning of 3 in L_5 so that the neighboring digits (i.e. 3s) are equal, so eliminate 3 from L_5 to get L_6 = {2,5,7,11}. Hence a(6) = 4.
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CROSSREFS
| Sequence in context: A017880 A086144 A131974 * A073792 A017870 A017860
Adjacent sequences: A062403 A062404 A062405 * A062407 A062408 A062409
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KEYWORD
| nonn,base
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 13 2002
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