A330447 a(n) is the smallest index k such that {0,1,2,...,n} is a subset of { A316774(j) : 0 <= j <= k }.

0, 1, 2, 5, 5, 8, 11, 22, 22, 32, 32, 42, 48, 48, 68, 71, 77, 89, 108, 115, 115, 140, 140, 149, 216, 268, 268, 268, 310, 310, 310, 340, 362, 362, 362, 362, 362, 476, 476, 476, 476, 560, 560, 560, 560, 560, 576, 576, 579, 692, 692, 707, 754, 794, 794, 797, 928

Offset: 0

Author

Alois P. Heinz, Dec 15 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A316774, A316905, A330448.

Programs

Maple

b:= proc() 0 end:
g:= proc(n) option remember; local t;
      t:= `if`(n<2, n, b(g(n-1))+b(g(n-2)));
      b(t):= b(t)+1; t
    end:
f:= proc() local t, a; t, a:= -1, proc() -1 end;
      proc(n) local h;
        while a(n) = -1 do
          t:= t+1; h:= g(t);
          if a(h) = -1 then a(h):= t fi
        od; a(n)
      end
    end():
a:= proc(n) option remember; `if`(n<0, 0,
      max(a(n-1), f(n)))
    end:
seq(a(n), n=0..100);

Mathematica

b[_] = 0;
g[n_] := g[n] = Module[{t}, t = If[n < 2, n, b[g[n - 1]] + b[g[n - 2]]]; b[t] = b[t] + 1; t];
f[n_] := Module[{t, a}, t = -1; a[_] = -1; Module[{h}, While[a[n] == -1, t = t + 1; h = g[t]; If[a[h] == -1, a[h] = t]]; a[n]]];
a[n_] := a[n] = If[n < 0, 0, Max[a[n - 1], f[n]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 13 2022, after Alois P. Heinz *)

Formula

a(n) = max_{0 <= j <= n} A316905(j).

a(n) >= A316905(n).

a(n) <= a(n+1).