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A250255 First row of spectral array W(e^gamma).

%I A250255 #7 Nov 16 2014 07:01:54
%S A250255 1,2,3,4,7,9,16,20,35,45,80,102,181,232,413,529,942,1206,2147,2750,
%T A250255 4897,6270,11167,14297,25463,32601,58064,74339,132403,169514,301916,
%U A250255 386541,688457,881425,1569881,2009905,3579786,4583168,8162954,10450956
%N A250255 First row of spectral array W(e^gamma).
%C A250255 Gamma is Euler's (or Euler-Mascheroni) constant.
%H A250255 A. Fraenkel and C. Kimberling, <a href="http://dx.doi.org/10.1016/0012-365X(94)90259-3">Generalized Wythoff arrays, shuffles and interspersions</a>, Discrete Mathematics 126 (1994) 137-149.
%o A250255 (PARI)
%o A250255 \\ Row i of the generalized Wythoff array W(h),
%o A250255 \\   where h is an irrational number between 1 and 2,
%o A250255 \\   and m is the number of terms in the vectors a and b.
%o A250255 row(h, i, m) = {
%o A250255   if(h<=1 || h>=2, print("Invalid value for h"); return);
%o A250255   my(
%o A250255     a=vector(m, n, floor(n*h)),
%o A250255     b=vector(m, n, floor(n*h/(h-1))),
%o A250255     w=[a[a[i]], b[a[i]]],
%o A250255     j=3
%o A250255   );
%o A250255   while(1,
%o A250255     if(j%2==1,
%o A250255       if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))
%o A250255     ,
%o A250255       if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))
%o A250255     );
%o A250255     j++
%o A250255   )
%o A250255 }
%o A250255 allocatemem(10^9)
%o A250255 row(exp(1)^Euler, 1, 10^7)
%Y A250255 Cf. A001620 (Gamma), A059565 (Corresponding Beatty sequence), A250253, A250254.
%K A250255 nonn
%O A250255 1,2
%A A250255 _Colin Barker_, Nov 15 2014