A007071 First row of 2-shuffle of spectral array W( sqrt 2 ). (Formerly M0616)

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

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..72.

Aviezri S. Fraenkel and Clark Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discr. Math. 126 (1-3) (1994) 137-149. [From R. J. Mathar, Aug 17 2009]

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) ; # R. J. Mathar, Aug 17 2009

Mathematica

WythSpec[n_, x_] :=  Floor[n*x] ;
A001951[n_] := WythSpec[n, Sqrt[2]];
A001952[n_] := A001951[n] + 2n;
WSqrt2[i_, j_] := WSqrt2[i, j] = Which[j == 1, A001951[A001951[i]], j == 2, A001952[A001951[i]], OddQ[j], A001951[WSqrt2[i, j-1]], True, A001952[WSqrt2[i, j-2]]];
A007071[n_] := A007071[n] = Module[{a, k}, If[n == 1, 1, For[a = A007071[n-1]+1, True, a++, For[k = 1, True, k++, If[WSqrt2[k, 1] == a, Return[a], If[WSqrt2[k, 1] > a, Break[]]]]; For[k = 1, True, k++, If[WSqrt2[k, 2] == a, Return[a], If[WSqrt2[k, 2] > a, Break[]]]]]]];
Table[A007071[n], {n, 1, 72}] (* Jean-François Alcover, Dec 20 2023, after R. J. Mathar *)

Crossrefs

Sequence in context: A057196 A080637 A124134 * A242482 A085784 A085783

Adjacent sequences: A007068 A007069 A007070 * A007072 A007073 A007074

Keyword

nonn,easy

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from R. J. Mathar, Aug 17 2009

Status

approved