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Search: id:A074049
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| A074049 |
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A permutation of the positive integers. |
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+0
3
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| 1, 2, 3, 5, 4, 7, 8, 13, 6, 10, 11, 18, 12, 20, 21, 34, 9, 15, 16, 26, 17, 28, 29, 47, 19, 31, 32, 52, 33, 54, 55, 89, 14, 23, 24, 39, 25, 41, 42, 68, 27, 44, 45, 73, 46, 75, 76, 123, 30, 49, 50, 81, 51, 83, 84, 136, 53, 86, 87, 141, 88, 143, 144, 233, 22, 36, 37
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Write t=tau=(1+sqrt(5))/2 and let S be generated by these rules: 1 is in S and if x is in S, then f(x) := [t*x] and g(x) := [(t+1)*x] are in S. Then S is the set of positive integers and the present permutation of S is obtained by arranging S in rows according to the order in which they are generated by f and g, starting with x=1.
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FORMULA
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Array T(n, k) by rows: T(0, 0)=1; T(1, 0)=2; T(n, 2j)=Floor(tau*T(n-1, j)) and T(n, 2j+1)=Floor((tau+1)*T(n-1, j)) for j=0, 1, ..., 2^(n-1)-1, n=2, 3, 4, ...
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EXAMPLE
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First rows: 1; 2; 3,5; 4,7,8,13; 6,10,11,18,12,20,21,34; ...
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CROSSREFS
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Cf. A074050.
Equals A048680(n-1) + 1.
Sequence in context: A127515 A099424 A117955 this_sequence A127521 A102399 A118318
Adjacent sequences: A074046 A074047 A074048 this_sequence A074050 A074051 A074052
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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), Aug 14 2002
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