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A351999
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A chain reaction sequence: a digit d1 from a(n) is expelled towards a(n+1) where it hits a digit d2 [from a(n+1)] and replaces it; d2 in turn is expelled towards a(n+2), hits a digit d3 there and replaces it; d3 in turn is expelled towards a(n+3), hits a digit there, and replaces it; d4 is expelled... etc. At the end of the chain reaction, only Fibonacci numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.
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4
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1, 2, 3, 4, 30, 610, 611, 5, 6, 110, 7, 307, 612, 8, 9, 80, 613, 10, 614, 31, 13, 20, 615, 15, 21, 22, 11, 23, 12, 41, 32, 51, 25, 61, 210, 71, 317, 24, 33, 14, 26, 310, 16, 410, 34, 35, 45, 36, 510, 50, 616, 710, 327, 81, 19, 27, 337, 17, 347, 37, 357, 52, 91, 82, 133, 28, 29, 233, 333, 18, 39, 44
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OFFSET
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1,2
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COMMENTS
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The sequence is a permutation of the integers > 0.
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LINKS
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EXAMPLE
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1 is expelled from a(1) = 1 and hits the 2 of a(2) = 2, "turning" this integer into 2, a Fibonacci number;
2 is expelled from a(2) = 2 and hits the 3 of a(3) = 3, "turning" this integer into 3, a Fibonacci number;
3 is expelled from a(3) = 3 and hits the 4 of a(4) = 4, turning this integer into 3, a Fibonacci number;
4 is expelled from a(4) = 4 and hits the 0 of a(5) = 30, turning this integer into 34, a Fibonacci number;
0 is expelled from a(5) = 30 and hits the 0 of a(6) = 610, "turning" this integer into 610, a Fibonacci number;
0 is expelled from a(6) = 610 and hits the rightmost 1 of a(7) = 611, turning this integer into 610, a Fibonacci number;
1 is expelled from a(7) = 611 and hits the 5 of a(8) = 5, turning this integer into 1, a Fibonacci number;
5 is expelled from a(8) = 5 and hits the 6 of a(9) = 6, turning this integer into 5, a Fibonacci number;
6 is expelled from a(9) = 110 and hits the leftmost 1 of a(7) = 110, turning this integer into 610, a Fibonacci number; etc.
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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