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 A126760 a(0) = 0, a(2n) = a(n), a(3n) = a(n), a(6n+1) = 2n + 1, a(6n+5) = 2n + 2. 18
 0, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 4, 1, 5, 3, 2, 1, 6, 1, 7, 2, 3, 4, 8, 1, 9, 5, 1, 3, 10, 2, 11, 1, 4, 6, 12, 1, 13, 7, 5, 2, 14, 3, 15, 4, 2, 8, 16, 1, 17, 9, 6, 5, 18, 1, 19, 3, 7, 10, 20, 2, 21, 11, 3, 1, 22, 4, 23, 6, 8, 12, 24, 1, 25, 13, 9, 7, 26, 5, 27, 2, 1, 14, 28, 3, 29, 15, 10, 4, 30, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS For further information see A126759, which provided the original motivation for this sequence. From Antti Karttunen, Jan 28 2015: (Start) The odd bisection of the sequence gives A253887, and the even bisection gives the sequence itself. A254048 gives the sequence obtained when this sequence is restricted to A007494 (numbers congruent to 0 or 2 mod 3). For all odd numbers k present in square array A135765, a(k) = the column index of k in that array. (End) A322026 and this sequence (without the initial zero) are ordinal transforms of each other. - Antti Karttunen, Feb 09 2019 LINKS Antti Karttunen, Table of n, a(n) for n = 0..19683 FORMULA a(n) = A126759(n)-1. [The original definition.] From Antti Karttunen, Jan 28 2015: (Start) a(0) = 0, a(2n) = a(n), a(3n) = a(n), a(6n+1) = 2n + 1, a(6n+5) = 2n + 2. Or with the last clause represented in another way: a(0) = 0, a(2n) = a(n), a(3n) = a(n), a(6n+1) = 2n + 1, a(6n-1) = 2n. Other identities. For all n >= 1: a(n) = A253887(A003602(n)). a(6n-3) = a(4n-2) = a(2n-1) = A253887(n). (End) a(n) = A249746(A003602(A064989(n))). - Antti Karttunen, Feb 04 2015 MATHEMATICA f[n_] := Block[{a}, a = 0; a = a = a = 1; a[x_] := Which[EvenQ@ x, a[x/2], Mod[x, 3] == 0, a[x/3], Mod[x, 6] == 1, 2 (x - 1)/6 + 1, Mod[x, 6] == 5, 2 (x - 5)/6 + 2]; Table[a@ i, {i, 0, n}]] (* Michael De Vlieger, Feb 03 2015 *) PROG (Scheme, with memoizing macro definec) (definec (A126760 n) (cond ((zero? n) n) ((even? n) (A126760 (/ n 2))) ((zero? (modulo n 3)) (A126760 (/ n 3))) ((= 1 (modulo n 6)) (+ 1 (/ (- n 1) 3))) (else (/ (+ n 1) 3)))) ;; Antti Karttunen, Jan 28 2015 (PARI) A126760(n)={n&&n\=3^valuation(n, 3)<

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Last modified October 16 18:38 EDT 2019. Contains 328102 sequences. (Running on oeis4.)