A249179 First row of spectral array W(3^(1/3)).

1, 3, 4, 9, 12, 29, 41, 94, 135, 306, 441, 997, 1437, 3251, 4688, 10602, 15290, 34574, 49864, 112751, 162615, 367699, 530313, 1199127, 1729440, 3910553, 5639993, 12752965

Offset: 1

Author

Colin Barker, Dec 03 2014

Keywords

• nonn
• more

Comments

3^(1/3) = 1.442249570307408382321638310780109588391869253499350577546416...

The sequence is generated from the Beatty sequence (A059539) and from the complement of the Beatty sequence (A059540) for 3^(1/3).

Links

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

Crossrefs

Cf. A059539, A059540.

Programs

PARI

\\ 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 b and c.
row(h, i, m) = {
  if(h<=1 || h>=2, print("Invalid value for h"); return);
  my(
    b=vector(m, n, floor(n*h)),       \\ Beatty sequence for h
    c=vector(m, n, floor(n*h/(h-1))), \\ Complement of b
    w=[b[b[i]], c[b[i]]],
    j=3
  );
  while(1,
    if(j%2==1,
      if(w[j-1]<=#b, w=concat(w, b[w[j-1]]), return(w))
    ,
      if(w[j-2]<=#c, w=concat(w, c[w[j-2]]), return(w))
    );
    j++
  )
}
allocatemem(10^9)
default(realprecision, 100)
row(3^(1/3), 1, 10^7)