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URL: https://oeis.org/A307723

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A307723
Naturally ordered prime factorization of n as a quasi-logarithmic word over the binary alphabet {1,0}.
2
10, 1100, 1010, 110100, 101100, 11011000, 101010, 11001100, 10110100, 1101101000, 10110010, 1101100100, 1011011000, 1100110100, 10101010, 1101010100, 1011001100, 110110011000, 1010110100, 110011011000
OFFSET
2,1
COMMENTS
Let m(n) be the number of digits (letters) in a(n).
m(n) = 2*A064097(n) = 2*(A073933(n)-1).
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.
FORMULA
a(1) is empty.
a(n) = concatenation(1, a(n-1), 0) if n is prime.
a(n) = concatenation_{k=1..A001222(n)} a(A307746(n,k)) if n is composite.
a(n) = concatenation(a(n/A088387(n)), a(A088387(n))) if n is composite.
EXAMPLE
The sequence begins:
n a(n)
-- -----------
1
2 10
3 1100
4 1010
5 110100
6 101100
7 11011000
8 101010
9 11001100
10 10110100
11 1101101000
12 10110010
...
CROSSREFS
KEYWORD
nonn,base
AUTHOR
I. V. Serov, Apr 24 2019
STATUS
approved