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A250255 First row of spectral array W(e^gamma). 2

%I #7 Nov 16 2014 07:01:54

%S 1,2,3,4,7,9,16,20,35,45,80,102,181,232,413,529,942,1206,2147,2750,

%T 4897,6270,11167,14297,25463,32601,58064,74339,132403,169514,301916,

%U 386541,688457,881425,1569881,2009905,3579786,4583168,8162954,10450956

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

%C Gamma is Euler's (or Euler-Mascheroni) constant.

%H 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 (PARI)

%o \\ Row i of the generalized Wythoff array W(h),

%o \\ where h is an irrational number between 1 and 2,

%o \\ and m is the number of terms in the vectors a and b.

%o row(h, i, m) = {

%o if(h<=1 || h>=2, print("Invalid value for h"); return);

%o my(

%o a=vector(m, n, floor(n*h)),

%o b=vector(m, n, floor(n*h/(h-1))),

%o w=[a[a[i]], b[a[i]]],

%o j=3

%o );

%o while(1,

%o if(j%2==1,

%o if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))

%o ,

%o if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))

%o );

%o j++

%o )

%o }

%o allocatemem(10^9)

%o row(exp(1)^Euler, 1, 10^7)

%Y Cf. A001620 (Gamma), A059565 (Corresponding Beatty sequence), A250253, A250254.

%K nonn

%O 1,2

%A _Colin Barker_, Nov 15 2014

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Last modified March 28 07:46 EDT 2024. Contains 371235 sequences. (Running on oeis4.)