A250254 First row of spectral array W(gamma^2+1).

1, 4, 5, 16, 21, 64, 85, 256, 341, 1024, 1365, 4097, 5462, 16393, 21854, 65594, 87448, 262467, 349915, 1050235, 1400150, 4202409, 5602558, 16815516

Offset: 1

Author

Colin Barker, Nov 15 2014

Keywords

• nonn
• more

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), A059557 (Corresponding Beatty sequence), A250253, A250255.

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(Euler^2+1, 1, 10^7)