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A361946
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If the base-4 expansion of n starts with the digit 1, then replace 2's by 3's and vice versa; if it starts with the digit 2, then replace 1's by 3's and vice versa; if it starts with the digit 3, then replace 1's by 2's and vice versa; a(0) = 0.
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2
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0, 1, 2, 3, 4, 5, 7, 6, 8, 11, 10, 9, 12, 14, 13, 15, 16, 17, 19, 18, 20, 21, 23, 22, 28, 29, 31, 30, 24, 25, 27, 26, 32, 35, 34, 33, 44, 47, 46, 45, 40, 43, 42, 41, 36, 39, 38, 37, 48, 50, 49, 51, 56, 58, 57, 59, 52, 54, 53, 55, 60, 62, 61, 63, 64, 65, 67, 66
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OFFSET
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0,3
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COMMENTS
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This sequence is a self-inverse permutation of the nonnegative integers.
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LINKS
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FORMULA
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a(n) = n iff n = d * A000695(k) for some d in {1, 2, 3} and some k >= 0.
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EXAMPLE
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For n = 539:
- the base-4 expansion of 539 is "20123",
- it starts with the digit 2, so we replace 1's by 3's and vice versa,
- so the base-4 expansion of a(539) is "20321", and a(539) = 569.
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PROG
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(PARI) a(n) = { my (q = digits(n, 4), m = if (#q, [ [0, 1, 3, 2], [0, 3, 2, 1], [0, 2, 1, 3] ][q[1]], [0, 1, 2, 3])); fromdigits(apply (d -> m[1+d], q), 4); }
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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