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A007071
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First row of 2-shuffle of spectral array W( sqrt 2 ).
(Formerly M0616)
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1
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1, 2, 3, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 35, 36, 37, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 59, 60, 61, 63, 64, 65, 67, 69, 70, 71, 73, 74, 75, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 93, 94, 95, 97, 98, 99, 101
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| A. Fraenkel and C. Kimberling, "Generalized Wythoff arrays, shuffles and interspersions," Discrete Mathematics 126 (1994) 137-149.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| A. S. Fraenkel, C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discr. Math. 126 (1-3) (1994) 137-149. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009]
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MAPLE
| Digits := 200 : WythSpec := proc(n, x) floor(n*x) ; end: A001951 := proc(n) WythSpec(n, sqrt(2)) ; end: A001952 := proc(n) A001951(n)+2*n; end: Wsqrt2 := proc(i, j) option remember ; if j = 1 then A001951(A001951(i)) ; elif j = 2 then A001952(A001951(i)) ; elif type(j, 'odd') then A001951(procname(i, j-1)) ; else A001952(procname(i, j-2)) ; fi; end: A007071 := proc(n) option remember ; local a; if n = 1 then 1; else for a from procname(n-1)+1 do for k from 1 do if Wsqrt2(k, 1) = a then RETURN(a); elif Wsqrt2(k, 1) > a then break; fi; od: for k from 1 do if Wsqrt2(k, 2) = a then RETURN(a); elif Wsqrt2(k, 2) > a then break; fi; od: od: fi; end: seq(A007071(n), n=1..100) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009]
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CROSSREFS
| Sequence in context: A057196 A080637 A124134 * A085784 A085783 A143664
Adjacent sequences: A007068 A007069 A007070 * A007072 A007073 A007074
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein (mira(AT)math.berkeley.edu)
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009
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