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A263390
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a(3n) = n, otherwise a(n) = a(floor(2n/3)).
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2
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0, 0, 0, 1, 0, 1, 2, 0, 1, 3, 2, 0, 4, 1, 3, 5, 2, 0, 6, 4, 1, 7, 3, 5, 8, 2, 0, 9, 6, 4, 10, 1, 7, 11, 3, 5, 12, 8, 2, 13, 0, 9, 14, 6, 4, 15, 10, 1, 16, 7, 11, 17, 3, 5, 18, 12, 8, 19, 2, 13, 20, 0, 9, 21, 14, 6, 22, 4, 15, 23, 10, 1, 24, 16, 7, 25
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OFFSET
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0,7
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COMMENTS
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This sequence is the unique fixed point of the function (a(0), a(1), a(2), ...) |--> (0, a(0), a(1), 1, a(2), a(3), 2, a(4), a(5), ...) which interleaves the nonnegative integers with pairs of elements of a sequence.
Compare with A025480, the unique fixed point of the function (a(0), a(1), a(2), ...) |--> (0, a(0), 1, a(1), 2, a(2), ...) which interleaves the nonnegative integers between the elements of a sequence.
These are the nim-values for heaps of n beans in the game where you're allowed to take up to one-third of the beans in a heap.
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LINKS
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FORMULA
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MATHEMATICA
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Nest[Append[#1, If[Mod[#2, 3] == 0, #2/3, #1[[Floor[2 #2/3] + 1]]]] & @@ {#, Length[#]} &, {0}, 75] (* Michael De Vlieger, Jul 09 2021 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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