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A098100
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Write each non-Fibonacci integer >0 on a single label. Put the labels in numerical order to form an infinite sequence L. Now consider the succession of single digits of A000045 (Fibonacci numbers): 1 1 2 3 5 8 1 3 2 1 3 4 5 5 8 9 1 4 4 2 3 3 3 7 7 6 1 0 9... The sequence S gives a rearrangement of the labels that reproduces the same succession of digits, subject to the constraint that the smallest label must be used that does not lead to a contradiction.
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0
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11, 23, 58, 132, 134, 558, 9, 14, 4, 2333, 7, 76, 10, 98, 71, 59, 72, 584, 41, 81, 6, 765, 109, 46, 17, 711, 28, 65, 74, 63, 68, 750, 25, 12, 139, 31, 96, 418, 317, 811, 51, 42, 29, 83, 20, 40, 1346, 26, 92, 178, 30, 93, 52, 45, 78, 570, 288, 79, 22, 746, 514, 930, 35
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OFFSET
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1,1
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COMMENTS
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This could be roughly rephrased like this: "Re-write in the most economical way the "Fibonacci pattern" using only non-Fibonacci numbers, but re-arranged. All the numbers of the sequence must be different one from another".
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LINKS
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EXAMPLE
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We must begin with 1,1,2... and we cannot represent "1" by 1 because this label doesn't exist (available labels carry only non-Fibonacci numbers), so the next possibility is the label "11". For 28657,46368,75025,... we cannot use label "75" in "28 65 74 63 68 75..." since no label begins with a 0. Labels of L cannot be used more than once.
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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