

A317015


a(n) = n for n < 2, a(n) = a(freq(a(n1),n)) + a(freq(a(n2),n)) for n >= 2, where freq(i, j) is the number of times i appears in the first j terms.


2



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, 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, 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
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OFFSET

0,3


COMMENTS

Inspired by A316774.
Let b(n) = n for n < 3, b(n) = b(freq(b(n1),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(n1),n) and freq(a(n2),n).


LINKS

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


MAPLE

b:= proc() 0 end:
a:= proc(n) option remember; local t;
t:= `if`(n<2, n, a(b(a(n1)))+a(b(a(n2))));
b(t):= b(t)+1; t
end:
seq(a(n), n=0..200); # Alois P. Heinz, Jul 19 2018


MATHEMATICA

Nest[Append[#, #[[Count[#, #[[1]] ] + 1]] + #[[Count[#, #[[2]] ] + 1 ]] ] &, {0, 1}, 95] (* Michael De Vlieger, Jul 20 2018 *)


CROSSREFS

Cf. A316774.
Sequence in context: A098086 A332887 A306323 * A175681 A161003 A152028
Adjacent sequences: A317012 A317013 A317014 * A317016 A317017 A317018


KEYWORD

nonn


AUTHOR

Altug Alkan, Jul 19 2018


STATUS

approved



