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

1, 6, 7, 37, 43, 233, 276, 1469, 1745, 9266, 11011, 58449, 69460, 368695, 438155, 2325725, 2763880, 14670658

Offset

1,2

Comments

1/sin(1) = 1.18839510577812121626159945237455100352782983409796262526525...

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

Links

Table of n, a(n) for n=1..18.

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

Prog

(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(1/sin(1), 1, 10^7)

Crossrefs

Cf. A108120, A108587.

Sequence in context: A175167 A027021 A013627 * A294728 A219212 A301904

Adjacent sequences: A248847 A248848 A248849 * A248851 A248852 A248853

Keyword

nonn,more

Author

Colin Barker, Dec 03 2014

Status

approved