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%I M0616 #22 Dec 21 2023 10:23:23
%S 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,
%T 36,37,39,40,41,43,45,46,47,49,50,51,53,54,55,57,59,60,61,63,64,65,67,
%U 69,70,71,73,74,75,77,79,80,81,83,84,85,87,88,89,91,93,94,95,97,98,99,101
%N First row of 2-shuffle of spectral array W( sqrt 2 ).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Aviezri S. Fraenkel and Clark Kimberling, <a href="http://dx.doi.org/10.1016/0012-365X(94)90259-3">Generalized Wythoff arrays, shuffles and interspersions</a>, Discr. Math. 126 (1-3) (1994) 137-149. [From _R. J. Mathar_, Aug 17 2009]
%p 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
%t WythSpec[n_, x_] := Floor[n*x] ;
%t A001951[n_] := WythSpec[n, Sqrt[2]];
%t A001952[n_] := A001951[n] + 2n;
%t 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]]];
%t 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[]]]]]]];
%t Table[A007071[n], {n, 1, 72}] (* _Jean-François Alcover_, Dec 20 2023, after _R. J. Mathar_ *)
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_
%E More terms from _R. J. Mathar_, Aug 17 2009
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