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%I #15 Feb 26 2023 08:18:50
%S 0,1,2,-1,3,-2,0,4,-3,-1,1,-4,5,-5,-2,0,-6,2,-7,-3,6,-8,-4,-1,-9,1,
%T -10,-5,3,-11,-6,-2,-12,7,-13,-7,-3,-14,0,-15,-8,2,-16,-9,-4,-17,4,
%U -18,-10,-5,-19,-1,-20,-11,8,-21,-12,-6,-22,-2,-23,-13,1,-24,-14,-7,-25,3,-26,-15,-8,-27,-3,-28,-16,5,-29,-17,-9,-30
%N Number of the diagonal of the Wythoff array that contains n.
%C Every integer occurs in this sequence (infinitely many times).
%C Represent the array as {g(i,j): i>=1, j>=1}. Then for m>=0, (diagonal #m) is the sequence (g(i,i+m)), i>=1; for m<0, (diagonal #m) is the sequence (g(i+m,i)), i>=1.
%e The main diagonal of the Wythoff array is (1,7,16,...); that's diagonal #0, so that a(1)=0, a(7)=0, a(16)=0.
%t f[n_]:=f[n]=Fibonacci[n];
%t g[i_,j_]:=f[j+1]*Floor[i*GoldenRatio]+(i-1) f[j];
%t t=Table[g[i,j],{i,500},{j,100}];
%t Map[#[[2]]-#[[1]]&,Most[Reap[NestWhileList[#+1&,1,Length[Sow[FirstPosition[t,#]]]>1&]][[2]][[1]]]] (* _Peter J. C. Moses_, Feb 09 2023 *)
%Y Cf. A035513, A114327, A191361, A191362.
%K sign
%O 1,3
%A _Clark Kimberling_, May 31 2011
%E Mathematica program replaced by _Clark Kimberling_, Feb 10 2023.
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