A330447 -id:A330447 - cp's OEIS frontend

A330448 a(n) = A330447(n) - A316905(n).

0, 0, 0, 0, 1, 0, 0, 0, 8, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 23, 0, 45, 0, 0, 0, 74, 8, 0, 56, 47, 0, 0, 105, 67, 85, 64, 0, 130, 45, 111, 0, 21, 136, 74, 98, 0, 97, 0, 0, 35, 0, 0, 0, 37, 0, 0, 0, 52, 0, 104, 52, 67, 0, 0, 70, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0

Offset: 0

Alois P. Heinz, Dec 15 2019

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

Cf. A316774, A316905, A330447.

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():
h:= proc(n) option remember; `if`(n<0, 0,
      max(h(n-1), f(n)))
    end:
a:= n-> h(n)-f(n):
seq(a(n), n=0..100);

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]]];
h[n_] := h[n] = If[n < 0, 0, Max[h[n - 1], f[n]]];
a[n_] := h[n] - f[n];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 13 2023, after Alois P. Heinz *)

A316905 a(n) is the index of the first occurrence of n in A316774.

Original entry on oeis.org

0, 1, 2, 5, 4, 8, 11, 22, 14, 32, 28, 42, 48, 45, 68, 71, 77, 89, 108, 115, 92, 140, 95, 149, 216, 268, 194, 260, 310, 254, 263, 340, 362, 257, 295, 277, 298, 476, 346, 431, 365, 560, 539, 424, 486, 462, 576, 479, 579, 692, 657, 707, 754, 794, 757, 797, 928

Offset: 0

Alois P. Heinz, Jul 18 2018

			a(4) = 4 because A316774(j) = 4 for j in {4,7,12,13,36,49,55} with minimal element 4.

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

Cf. A316774, A316973, A316984, A330440 (a sorted version of this), A330447, A330448.

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:
a:= 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():
seq(a(n), n=0..100);

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];
a[n_] := Module[{t = -1, a}, a[_] = -1; Module[{h}, While[a[n] == -1, t = t + 1; h = g[t]; If[a[h] == -1, a[h] = t]]; a[n]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 28 2023, after Alois P. Heinz *)

a(n) = min { j >= 0 : A316774(j) = n }.

cp's OEIS Frontend

A330448 a(n) = A330447(n) - A316905(n).

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