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Search: id:A002251
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| A002251 |
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Start with sequence of nonnegative integers; then swap L(k) and U(k) for all k >= 1, where L = A000201, U = A001950 (lower and upper Wythoff sequences). |
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+0
15
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| 0, 2, 1, 5, 7, 3, 10, 4, 13, 15, 6, 18, 20, 8, 23, 9, 26, 28, 11, 31, 12, 34, 36, 14, 39, 41, 16, 44, 17, 47, 49, 19, 52, 54, 21, 57, 22, 60, 62, 24, 65, 25, 68, 70, 27, 73, 75, 29, 78, 30, 81, 83, 32, 86, 33, 89, 91, 35, 94, 96, 37, 99, 38, 102, 104, 40, 107, 109
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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(n,a(n)) are Wythoff pairs: (0,0),(1,2),(3,5),(4,7),..., where each difference occurs once.
Self-inverse when considered as a permutation or function, i.e. a(a(n)) = n. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
If the offset is 1, the sequence can also be obtained by rearranging the natural numbers so that sum of n terms is a multiple of n, or equivalently so that the arithmetic mean of the first n terms is an integer. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 16 2002
For n=1,2,3,..., let p(n)=least natural number not already an a(k), q(n)=n+p(n); then a(p(n))=q(n), a(q(n))=p(n). - Clark Kimberling (ck6(AT)evansville.edu)
Also, indices of powers of 2 in A086482. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 26 2003
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 76.
R. Silber, Wythoff's Nim and Fibonacci Representations, Fibonacci Quarterly #14 (1977), pp. 85-88.
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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CROSSREFS
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A002251 maps between A000201 and A001950, in that A002251(A000201(n)) = A001950(n), A002251(A001950(n)) = A000201(n). A019444 = A002251 + 1.
Row 0 of A018219. Cf. A073869.
Sequence in context: A059039 A109261 A085240 this_sequence A093545 A005297 A014551
Adjacent sequences: A002248 A002249 A002250 this_sequence A002252 A002253 A002254
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Michael Kleber, michael.kleber(AT)gmail.com
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EXTENSIONS
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Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 29 2002
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