A022161 -id:A022161 - cp's OEIS frontend

A022160 First column of spectral array W(e-1).

1, 5, 8, 10, 13, 17, 20, 22, 25, 29, 30, 34, 37, 41, 42, 46, 49, 51, 54, 58, 61, 63, 67, 70, 72, 75, 79, 82, 84, 87, 91, 92, 96, 99, 103, 104, 108, 111, 115, 116, 120, 123, 125, 128, 132, 135, 137, 140, 144, 146, 149, 152, 156, 158, 161, 164, 166, 170, 173

Offset: 1

Clark Kimberling

nonn

G. C. Greubel, Table of n, a(n) for n = 1..5000
A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.

Cf. A022161.

[Floor((Exp(1)-1)*Floor(n*(Exp(1)-1))): n in [1..50]]; // G. C. Greubel, May 27 2018

Table[Floor[(E - 1)*Floor[(E - 1)*n]], {n, 1, 50}] (* G. C. Greubel, May 27 2018 *)

a(n) = floor((exp(1)-1)*floor((exp(1)-1)*n)); \\ Michel Marcus, Mar 05 2014

More terms from Michel Marcus, Mar 05 2014

A249309 First row of spectral array W(Pi/2).

Original entry on oeis.org

1, 2, 3, 5, 7, 13, 20, 35, 54, 96, 150, 264, 414, 726, 1140, 1997, 3136, 5495, 8631, 15121, 23752, 41612, 65363, 114513, 179876, 315132, 495008, 867223, 1362230, 2386544, 3748774, 6567622, 10316396

Offset: 1

Colin Barker, Oct 25 2014

nonn

A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.

Cf. A007068, A022159, A022161, A022163, A022165.

\\ The first row of the generalized Wythoff array W(h),
\\   where h is an irrational number between 1 and 2.
row1(h, m) = {
  my(
    a=vector(m, n, floor(n*h)),
    b=setminus(vector(m, n, n), a),
    w=[a[1]^2, b[a[1]]],
    j=3
  );
  while(1,
    if(j%2==1,
      if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))
    ,
      if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))
    );
    j++
  );
  w
}
allocatemem(10^9)
row1(Pi/2, 10^7)

A249697 First row of spectral array W(Pi-2).

Original entry on oeis.org

1, 8, 9, 64, 73, 516, 589, 4160, 4749, 33540, 38289, 270416, 308704, 2180232, 2488936, 17578149

Offset: 1

Colin Barker, Nov 04 2014

A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.

Cf. A007068, A022159, A022161, A022163, A022165, A249309.

\\ Row i of the generalized Wythoff array W(h),
\\ where h is an irrational number between 1 and 2,
\\ and m is the number of terms in the vectors a and b.
row(h, i, m) = {
  my(
    a=vector(m, n, floor(n*h)),
    b=vector(m, n, floor(n*h/(h-1))),
    w=[a[a[i]], b[a[i]]],
    j=3
  );
  while(1,
    if(j%2==1,
      if(w[j-1]<=#a, w=concat(w, a[w[j-1]]), return(w))
    ,
      if(w[j-2]<=#b, w=concat(w, b[w[j-2]]), return(w))
    );
    j++
  )
}
allocatemem(10^9)
row(Pi-2, 1, 10^7)

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A022160 First column of spectral array W(e-1).

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A249309 First row of spectral array W(Pi/2).

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A249697 First row of spectral array W(Pi-2).

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