A250254 -id:A250254 - cp's OEIS frontend

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

Colin Barker, Nov 15 2014

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

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

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

\\ 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)

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

Original entry on oeis.org

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

Colin Barker, Nov 15 2014

nonn

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

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

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

\\ 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)

cp's OEIS Frontend

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

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