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A330447
a(n) is the smallest index k such that {0,1,2,...,n} is a subset of { A316774(j) : 0 <= j <= k }.
3
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
0,3
LINKS
FORMULA
a(n) = max_{0 <= j <= n} A316905(j).
a(n) >= A316905(n).
a(n) <= a(n+1).
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 15 2019
STATUS
approved