A250253 First row of spectral array W(gamma+1).

1, 2, 3, 5, 7, 13, 20, 35, 55, 95, 149, 259, 408, 707, 1115, 1931, 3045, 5276, 8321, 14416, 22737, 39391, 62128, 107634, 169762, 294105, 463867, 803628, 1267494, 2195877, 3463371, 6000134, 9463505, 16395094

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..34.

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 a and b.
row(h, i, m) = {
  if(h<=1 || h>=2, print("Invalid value for h"); return);
  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(Euler+1, 1, 10^7)

Crossrefs

Cf. A001620 (Gamma), A059555 (Corresponding Beatty sequence), A250254, A250255.

Sequence in context: A294443 A293160 A249309 * A119717 A000627 A337270

Adjacent sequences: A250250 A250251 A250252 * A250254 A250255 A250256

Keyword

nonn,more

Author

Colin Barker, Nov 15 2014

Status

approved