cp's OEIS Frontend

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

%I A330447 #17 Oct 13 2022 11:09:46
%S A330447 0,1,2,5,5,8,11,22,22,32,32,42,48,48,68,71,77,89,108,115,115,140,140,
%T A330447 149,216,268,268,268,310,310,310,340,362,362,362,362,362,476,476,476,
%U A330447 476,560,560,560,560,560,576,576,579,692,692,707,754,794,794,797,928
%N A330447 a(n) is the smallest index k such that {0,1,2,...,n} is a subset of { A316774(j) : 0 <= j <= k }.
%H A330447 Alois P. Heinz, <a href="/A330447/b330447.txt">Table of n, a(n) for n = 0..20000</a>
%F A330447 a(n) = max_{0 <= j <= n} A316905(j).
%F A330447 a(n) >= A316905(n).
%F A330447 a(n) <= a(n+1).
%p A330447 b:= proc() 0 end:
%p A330447 g:= proc(n) option remember; local t;
%p A330447       t:= `if`(n<2, n, b(g(n-1))+b(g(n-2)));
%p A330447       b(t):= b(t)+1; t
%p A330447     end:
%p A330447 f:= proc() local t, a; t, a:= -1, proc() -1 end;
%p A330447       proc(n) local h;
%p A330447         while a(n) = -1 do
%p A330447           t:= t+1; h:= g(t);
%p A330447           if a(h) = -1 then a(h):= t fi
%p A330447         od; a(n)
%p A330447       end
%p A330447     end():
%p A330447 a:= proc(n) option remember; `if`(n<0, 0,
%p A330447       max(a(n-1), f(n)))
%p A330447     end:
%p A330447 seq(a(n), n=0..100);
%t A330447 b[_] = 0;
%t A330447 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];
%t A330447 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]]];
%t A330447 a[n_] := a[n] = If[n < 0, 0, Max[a[n - 1], f[n]]];
%t A330447 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Oct 13 2022, after _Alois P. Heinz_ *)
%Y A330447 Cf. A316774, A316905, A330448.
%K A330447 nonn
%O A330447 0,3
%A A330447 _Alois P. Heinz_, Dec 15 2019