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 A329101 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of 1's in the base 4 expansion of n equals the number of 2's in the base 4 expansion of a(n). 2
 0, 2, 1, 3, 6, 10, 8, 9, 4, 11, 5, 7, 12, 14, 13, 15, 18, 26, 22, 24, 34, 42, 38, 40, 25, 41, 27, 30, 32, 43, 33, 35, 16, 36, 17, 19, 37, 46, 39, 44, 20, 45, 21, 23, 28, 47, 29, 31, 48, 50, 49, 51, 54, 58, 56, 57, 52, 59, 53, 55, 60, 62, 61, 63, 66, 74, 70, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence is a permutation of the nonnegative integers with inverse A329180. Apparently, fixed points correspond to A001196. The sequence has fractal features; for any k >= 0, the set of points { (n, a(n)), n = 0..4^k-1 } is symmetrical relative to the line of equation y + x = 4^k - 1 (see scatterplots in Links section). LINKS Rémy Sigrist, Table of n, a(n) for n = 0..4095 Rémy Sigrist, PARI program for A329101 Rémy Sigrist, Scatterplot of the sequence for n = 0..4^3-1 Rémy Sigrist, Scatterplot of the sequence for n = 0..4^10-1 Rémy Sigrist, Colored scatterplot of the sequence for n = 0..4^10-1 (where the color is function of A160381(n)) Index entries for sequences that are permutations of the natural numbers FORMULA A160381(n) = A160382(a(n)). EXAMPLE The first terms, alongside the base 4 representations of n and of a(n), are: n a(n) qua(n) qua(a(n)) -- ---- ------ --------- 0 0 0 0 1 2 1 2 2 1 2 1 3 3 3 3 4 6 10 12 5 10 11 22 6 8 12 20 7 9 13 21 8 4 20 10 9 11 21 23 10 5 22 11 11 7 23 13 12 12 30 30 13 14 31 32 14 13 32 31 15 15 33 33 PROG (PARI) See Links section. CROSSREFS Cf. A001196, A160381, A160382, A329180. Sequence in context: A086964 A076242 A066203 * A024866 A076058 A098124 Adjacent sequences: A329098 A329099 A329100 * A329102 A329103 A329104 KEYWORD nonn,base AUTHOR Rémy Sigrist, Nov 07 2019 STATUS approved

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Last modified June 5 02:46 EDT 2023. Contains 363130 sequences. (Running on oeis4.)