A317015 - OEIS

%I #20 Jul 22 2018 14:35:11

%S 0,1,2,2,4,3,2,3,4,4,4,8,5,2,5,6,3,3,8,6,4,5,5,8,6,4,4,6,7,5,4,7,6,5,

%T 5,6,5,6,7,5,6,8,8,6,7,8,6,6,16,9,2,4,7,7,4,6,9,7,5,7,8,7,7,8,8,8,8,

%U 16,10,3,4,11,9,3,4,7,13,9,5,12,9,4,5,7,10,7,4,7,10,7,8,11,7,5,5,10,9

%N a(n) = n for n < 2, a(n) = a(freq(a(n-1),n)) + a(freq(a(n-2),n)) for n >= 2, where freq(i, j) is the number of times i appears in the first j terms.

%C Inspired by A316774.

%C Let b(n) = n for n < 3, b(n) = b(freq(b(n-1),n)) for n >= 3, where freq(i, j) is the number of times i appears in the first j terms and b(n) has offset 0. For n >= 1, b(n) - 1 are 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, ... (cf. A093879). While b(n) has one parent spot, this entry (a(n)) has two parent spots which are freq(a(n-1),n) and freq(a(n-2),n).

%H Alois P. Heinz, <a href="/A317015/b317015.txt">Table of n, a(n) for n = 0..65536</a>

%p b:= proc() 0 end:

%p a:= proc(n) option remember; local t;

%p       t:= `if`(n<2, n, a(b(a(n-1)))+a(b(a(n-2))));

%p       b(t):= b(t)+1; t

%p     end:

%p seq(a(n), n=0..200);  # _Alois P. Heinz_, Jul 19 2018

%t Nest[Append[#, #[[Count[#, #[[-1]] ] + 1]] + #[[Count[#, #[[-2]] ] + 1 ]] ] &, {0, 1}, 95] (* _Michael De Vlieger_, Jul 20 2018 *)

%Y Cf. A316774.

%K nonn

%O 0,3

%A _Altug Alkan_, Jul 19 2018