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 A298196 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the 2-adic valuation of a(n) equals the 3-adic valuation of a(n+1). 3
 1, 2, 3, 4, 9, 5, 7, 8, 27, 10, 6, 12, 18, 15, 11, 13, 14, 21, 16, 81, 17, 19, 20, 36, 45, 22, 24, 54, 30, 33, 23, 25, 26, 39, 28, 63, 29, 31, 32, 243, 34, 42, 48, 162, 51, 35, 37, 38, 57, 40, 108, 72, 135, 41, 43, 44, 90, 60, 99, 46, 66, 69, 47, 49, 50, 75 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The 2-adic and 3-adic valuations of a number are respectively given by A007814 and by A007949. For any distinct prime numbers p and q, let F_{p,q} be the lexicographically earliest sequence of distinct positive terms such that for any n > 0, the p-adic valuation of F_{p,q}(n) equals the q-adic valuation of F_{p,q}(n+1): - in particular, F_{2,3} = a (this sequence) and F_{3,2} = A304881, - the powers of q appear in order in F_{p,q}, - every power of q appear in F_{p,q}, - F_{p,q} is a permutation of the natural numbers. This sequence is a permutation of the natural numbers, with inverse A304872. The first known fixed points are: 1, 2, 3, 4, 7, 8, 10, 12, 42. LINKS Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms (where the color is function of A007949(a(n))) Rémy Sigrist, PARI program for A298196 EXAMPLE The first terms, alongside their 2-adic and 3-adic valuations, are: n a(n) v2 v3 -- ---- -- -- 1 1 0 0 2 2 1 0 3 3 0 1 4 4 2 0 5 9 0 2 6 5 0 0 7 7 0 0 8 8 3 0 9 27 0 3 10 10 1 0 11 6 1 1 12 12 2 1 13 18 1 2 14 15 0 1 15 11 0 0 16 13 0 0 17 14 1 0 18 21 0 1 19 16 4 0 20 81 0 4 PROG (PARI) See Links section. CROSSREFS Cf. A007814, A007949, A304872 (inverse), A304881. Sequence in context: A326776 A249746 A112480 * A112095 A260435 A255554 Adjacent sequences: A298193 A298194 A298195 * A298197 A298198 A298199 KEYWORD nonn AUTHOR Rémy Sigrist, May 19 2018 STATUS approved

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Last modified March 29 12:22 EDT 2023. Contains 361599 sequences. (Running on oeis4.)