A317359 -id:A317359 - cp's OEIS frontend

A317361 a(n) is the index of the first occurrence of n in A317359.

0, 1, 3, 6, 10, 39, 45, 25, 17, 527, 537, 55, 34, 134, 197, 309, 636, 66, 97, 555, 176, 2100, 285, 4247, 4499, 155, 8729, 591, 325, 1144, 1124, 4379, 211, 2331, 8534, 8573, 341, 609, 8482, 225, 1344, 9418, 4163, 34510, 357, 780, 239, 2122, 4583, 1204, 1544, 2683, 373, 253, 4211, 654, 45895, 33400, 2144

Offset: 0

Altug Alkan, Jul 26 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..6244

Cf. A317359.

A317369 a(0) = 0, a(1) = 1; for n >= 2, a(n) = freq(a(n-s(n)),n) where s = A000196 and freq(i, j) is the number of times i appears in the terms a(0) .. a(j-1).

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 3, 3, 2, 2, 2, 6, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 13, 13, 13, 13, 13, 13, 6, 6, 6, 6, 6, 6, 6, 20, 20, 20, 20, 20, 20, 20, 7, 7, 7, 7, 7, 7, 7, 7, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

Altug Alkan, Jul 26 2018

nonn

Altug Alkan, A line graph of a(n) for n <= 50000
Altug Alkan, A line graph of a(n) - A000196(n) + 1

Cf. A000196, A028391, A317223, A317359.

Nest[Append[#1, Count[#1, #1[[-Floor@ Sqrt@ #2]] ]] & @@ {#, Length@ #} &, {0, 1}, 92] (* Michael De Vlieger, Jul 27 2018 *)

A317389 a(0) = 0, a(1) = a(2) = 1; for n >= 3, a(n) = freq(a(g(n)),n)*freq(a(n-g(n)),n) where g = A000195 and freq(i, j) is the number of times i appears in the terms a(0) .. a(j-1).

Original entry on oeis.org

0, 1, 1, 4, 2, 2, 4, 4, 6, 6, 4, 4, 10, 10, 4, 4, 14, 14, 4, 4, 18, 81, 81, 9, 18, 18, 9, 27, 27, 18, 18, 18, 54, 54, 54, 27, 27, 27, 45, 45, 45, 27, 27, 27, 72, 72, 72, 27, 27, 27, 99, 99, 99, 27, 27, 6, 6, 26, 26, 8, 8, 4, 4, 4, 4, 26, 26, 26, 26, 12, 12, 12, 12, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16, 8, 8, 8, 8, 20, 20, 20

Offset: 0

Altug Alkan, Jul 27 2018

Alois P. Heinz, Table of n, a(n) for n = 0..65536

Cf. A317359.

b:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= `if`(n<3, n*(3-n)/2, b(a(ilog(n)))*b(a(n-ilog(n))));
      b(t):= b(t)+1; t
    end:
seq(a(n), n=0..200);  # Alois P. Heinz, Jul 27 2018

b[_] = 0;
a[n_] := a[n] = Module[{t}, t = If[n<3, n(3-n)/2, b[a[Floor@Log[n]]] b[a[n - Floor@Log[n]]]]; b[t] = b[t]+1; t];
a /@ Range[0, 200] (* Jean-François Alcover, Nov 27 2020, after Alois P. Heinz *)

cp's OEIS Frontend

A317361 a(n) is the index of the first occurrence of n in A317359.

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A317369 a(0) = 0, a(1) = 1; for n >= 2, a(n) = freq(a(n-s(n)),n) where s = A000196 and freq(i, j) is the number of times i appears in the terms a(0) .. a(j-1).

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A317389 a(0) = 0, a(1) = a(2) = 1; for n >= 3, a(n) = freq(a(g(n)),n)*freq(a(n-g(n)),n) where g = A000195 and freq(i, j) is the number of times i appears in the terms a(0) .. a(j-1).

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Mathematica