cp's OEIS Frontend

A307723 Naturally ordered prime factorization of n as a quasi-logarithmic word over the binary alphabet {1,0}.

%I A307723 #73 May 14 2019 11:10:04
%S A307723 10,1100,1010,110100,101100,11011000,101010,11001100,10110100,
%T A307723 1101101000,10110010,1101100100,1011011000,1100110100,10101010,
%U A307723 1101010100,1011001100,110110011000,1010110100,110011011000
%N A307723 Naturally ordered prime factorization of n as a quasi-logarithmic word over the binary alphabet {1,0}.
%C A307723 Let m(n) be the number of digits (letters) in a(n).
%C A307723 m(n) = 2*A064097(n) = 2*(A073933(n)-1).
%C A307723 Split the word a(n) into two parts of equal length. The number of 1's in the left part equals the number of 0's in the right part and vice versa.
%H A307723 I. V. Serov, <a href="/A307723/b307723.txt">Table of n, a(n) for n = 2..10000</a>
%F A307723 a(1) is empty.
%F A307723 a(n) = concatenation(1, a(n-1), 0) if n is prime.
%F A307723 a(n) = concatenation_{k=1..A001222(n)} a(A307746(n,k)) if n is composite.
%F A307723 a(n) = concatenation(a(n/A088387(n)), a(A088387(n))) if n is composite.
%e A307723 The sequence begins:
%e A307723    n a(n)
%e A307723   -- -----------
%e A307723    1
%e A307723    2 10
%e A307723    3 1100
%e A307723    4 1010
%e A307723    5 110100
%e A307723    6 101100
%e A307723    7 11011000
%e A307723    8 101010
%e A307723    9 11001100
%e A307723   10 10110100
%e A307723   11 1101101000
%e A307723   12 10110010
%e A307723   ...
%Y A307723 Cf. A010051, A088387, A307641, A307746, A064097, A073933.
%K A307723 nonn,base
%O A307723 2,1
%A A307723 _I. V. Serov_, Apr 24 2019