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A297352
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a(n) is the smallest positive number not yet in the sequence that if n is even, contains the smallest digit in a(n-1), and if n is odd, contains the largest digit in a(n-1); a(1)=0.
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5
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0, 10, 1, 11, 12, 13, 3, 23, 30, 20, 2, 21, 22, 24, 4, 14, 34, 31, 32, 25, 5, 15, 35, 33, 36, 37, 7, 17, 27, 26, 6, 16, 46, 40, 41, 18, 8, 28, 38, 39, 9, 19, 29, 42, 43, 53, 45, 44, 47, 48, 58, 50, 51, 61, 56, 52, 54, 49, 59, 55, 57, 65, 60, 70, 67, 62, 63, 73, 71, 81
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OFFSET
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1,2
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COMMENTS
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The 1-digit numbers appear in the sequence in the following order: 0,1,3,2,4,5,7,6,8,9.
After the first initial terms, the sequence oscillates about the line y=x.
The first differences are bounded by 30 and -30 for the initial terms, then by 20 and -20. After the first 122 terms the sequence is bounded most of the time by 10 and -10, with eventual jumps that seem to remain bounded by 30 and -30.
Inverse: 1, 3, 11, 7, 15, 21, 31, 27, 37, 41, 2, 4, 5, 6, 16, 22, 32, 28, 36, 42, 10, 12, 13, 8, 14, 20, ..., . - Robert G. Wilson v, Dec 29 2017
Also: a(0) = 0 (and 0 counts as a digit). For n > 0, if n is odd respectively even then a(n) is the smallest integer not already in the sequence that contains the smallest respectively largest digit of a(n - 1). - David A. Corneth, Dec 29 2017
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LINKS
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EXAMPLE
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a(2)=10 since it is the smallest number not yet in the sequence that contains the smallest digit in a(1)=0; a(3)=1 since it is the smallest number not yet in the sequence that contains the largest digit in a(2)=10.
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MATHEMATICA
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a[n_] := a[n] = Block[{k = 1, s = Union[IntegerDigits[a[n - 1]]][[If[ OddQ@ n, -1, 1]]], t = Array[a, n -1]}, While[ MemberQ[t, k] || !MemberQ[ IntegerDigits@ k, s], k++]; k]; a[1] = 0; Array[a, 70] (* Robert G. Wilson v, Dec 29 2017 *)
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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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EXTENSIONS
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STATUS
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approved
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