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Search: id:A115094
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| A115094 |
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Permutation of N based on lower Wythoff sequence. |
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+0
1
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| 3, 2, 1, 6, 5, 4, 7, 9, 8, 10, 12, 11, 13, 16, 15, 14, 19, 18, 17, 20, 22, 21, 23, 25, 24, 26, 29, 28, 27, 32, 31, 30, 35, 34, 33, 36, 38, 37, 39, 42, 41, 40, 45, 44, 43, 48, 47, 46, 49, 51, 50, 52, 55, 54, 53, 58, 57, 56, 61, 60, 59, 62, 64, 63, 65, 67, 66, 68, 71, 70, 69, 74
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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(1) a(n)=n if and only if n is in the upper Wythoff sequence, A001950. (2) This is a self-inverse permutation of N. (3) a(n)-n is one of -2,-1,0,1,2 for every n, and each of these occurs infinitely many times. (4) The sequence a(n)-n is a nonperiodic tiling of N.
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FORMULA
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Let L be the lower Wythoff sequence, A000201. Then a(n)=n if n is not any L(k), a(n)=L(k+1) if n=L(k) for odd k, a(n)=L(k-1) if n=L(k) for even k.
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EXAMPLE
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a(1)=3=L(1+1) because 1=L(1).
a(2)=2 because 2 is not in L.
a(3)=1=L(2-1) because 3=L(2).
a(4)=6=L(3+1) because 4=L(3).
a(6)=4=L(4-1) because 6=L(4).
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CROSSREFS
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Cf. A000201, A001950, A002251.
Sequence in context: A031252 A129674 A120771 this_sequence A113655 A114155 A079513
Adjacent sequences: A115091 A115092 A115093 this_sequence A115095 A115096 A115097
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Mar 02 2006
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