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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS I. V. Serov, Table of n, a(n) for n = 2..10000 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 Cf. A010051, A088387, A307641, A307746, A064097, A073933. Sequence in context: A069886 A133383 A268229 * A071672 A290155 A265849 Adjacent sequences: A307720 A307721 A307722 * A307724 A307725 A307726 KEYWORD nonn,base AUTHOR I. V. Serov, Apr 24 2019 STATUS approved

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Last modified September 29 19:17 EDT 2023. Contains 365776 sequences. (Running on oeis4.)