A250255 First row of spectral array W(e^gamma).

1, 2, 3, 4, 7, 9, 16, 20, 35, 45, 80, 102, 181, 232, 413, 529, 942, 1206, 2147, 2750, 4897, 6270, 11167, 14297, 25463, 32601, 58064, 74339, 132403, 169514, 301916, 386541, 688457, 881425, 1569881, 2009905, 3579786, 4583168, 8162954, 10450956

Offset: 1

Author

Colin Barker, Nov 15 2014

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A001620 (Gamma), A059565 (Corresponding Beatty sequence), A250253, A250254.

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 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(exp(1)^Euler, 1, 10^7)