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A250254 First row of spectral array W(gamma^2+1).

%I A250254 #8 Nov 16 2014 07:01:57
%S A250254 1,4,5,16,21,64,85,256,341,1024,1365,4097,5462,16393,21854,65594,
%T A250254 87448,262467,349915,1050235,1400150,4202409,5602558,16815516
%N A250254 First row of spectral array W(gamma^2+1).
%C A250254 Gamma is Euler's (or Euler-Mascheroni) constant.
%H A250254 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 A250254 (PARI)
%o A250254 \\ Row i of the generalized Wythoff array W(h),
%o A250254 \\   where h is an irrational number between 1 and 2,
%o A250254 \\   and m is the number of terms in the vectors a and b.
%o A250254 row(h, i, m) = {
%o A250254   if(h<=1 || h>=2, print("Invalid value for h"); return);
%o A250254   my(
%o A250254     a=vector(m, n, floor(n*h)),
%o A250254     b=vector(m, n, floor(n*h/(h-1))),
%o A250254     w=[a[a[i]], b[a[i]]],
%o A250254     j=3
%o A250254   );
%o A250254   while(1,
%o A250254     if(j%2==1,
%o A250254       if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))
%o A250254     ,
%o A250254       if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))
%o A250254     );
%o A250254     j++
%o A250254   )
%o A250254 }
%o A250254 allocatemem(10^9)
%o A250254 row(Euler^2+1, 1, 10^7)
%Y A250254 Cf. A001620 (Gamma), A059557 (Corresponding Beatty sequence), A250253, A250255.
%K A250254 nonn,more
%O A250254 1,2
%A A250254 _Colin Barker_, Nov 15 2014