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A276227
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The successive absolute differences of the "mixed" pairs rebuild the starting sequence (see Comments for the definition of a "mixed pair").
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1
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1, 2, 3, 5, 7, 9, 4, 6, 8, 10, 12, 14, 11, 13, 17, 19, 23, 18, 15, 16, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 29, 31, 37, 41, 43, 47, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 53, 59, 61, 67, 71, 65, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 73, 79, 83, 89, 97, 87, 82, 84, 85, 86, 88, 90, 91, 92
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OFFSET
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1,2
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COMMENTS
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A "mixed pair" happens when a(n) and a(n+1) share exactly one prime.
The sequence starts with a(1) = 1 and is always extended with the
smallest integer not yet used that doesn't lead to a contradiction.
The sequence is a permutation of the natural numbers.
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LINKS
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EXAMPLE
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The "mixed pairs" are between parentheses:
(1,2),3,5,(7,9),4,6,8,10,12,(14,11),13,17,19,(23,18),15,16,20,21,22,24,25,26,27,28,30,32,33,34,35,(36,29),...
Listing the absolute differences of those parentheses gives: (1),(2),(3),(5),(7),... which is indeed the starting sequence.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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