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A248850 First row of spectral array W(1/sin(1)). 0

%I #16 Dec 14 2014 02:50:16

%S 1,6,7,37,43,233,276,1469,1745,9266,11011,58449,69460,368695,438155,

%T 2325725,2763880,14670658

%N First row of spectral array W(1/sin(1)).

%C 1/sin(1) = 1.18839510577812121626159945237455100352782983409796262526525...

%C The sequence is generated from the Beatty sequence (A108120) and from the complement of the Beatty sequence (A108587) for 1/sin(1).

%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 b and c.

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

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

%o my(

%o b=vector(m, n, floor(n*h)), \\ Beatty sequence for h

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

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

%o j=3

%o );

%o while(1,

%o if(j%2==1,

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

%o ,

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

%o );

%o j++

%o )

%o }

%o allocatemem(10^9)

%o default(realprecision, 100)

%o row(1/sin(1), 1, 10^7)

%Y Cf. A108120, A108587.

%K nonn,more

%O 1,2

%A _Colin Barker_, Dec 03 2014

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)