cp's OEIS Frontend

A317015 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.

%I A317015 #20 Jul 22 2018 14:35:11
%S A317015 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 A317015 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 A317015 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 A317015 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 A317015 Inspired by A316774.
%C A317015 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 A317015 Alois P. Heinz, <a href="/A317015/b317015.txt">Table of n, a(n) for n = 0..65536</a>
%p A317015 b:= proc() 0 end:
%p A317015 a:= proc(n) option remember; local t;
%p A317015       t:= `if`(n<2, n, a(b(a(n-1)))+a(b(a(n-2))));
%p A317015       b(t):= b(t)+1; t
%p A317015     end:
%p A317015 seq(a(n), n=0..200);  # _Alois P. Heinz_, Jul 19 2018
%t A317015 Nest[Append[#, #[[Count[#, #[[-1]] ] + 1]] + #[[Count[#, #[[-2]] ] + 1 ]] ] &, {0, 1}, 95] (* _Michael De Vlieger_, Jul 20 2018 *)
%Y A317015 Cf. A316774.
%K A317015 nonn
%O A317015 0,3
%A A317015 _Altug Alkan_, Jul 19 2018