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A297353
a(n) is the smallest positive number not yet in the sequence that if n is odd, contains the smallest digit in a(n-1), and if n is even, contains the largest digit in a(n-1); a(1)=0.
5
0, 10, 20, 2, 12, 21, 1, 11, 13, 3, 23, 30, 40, 4, 14, 24, 22, 25, 26, 6, 16, 36, 31, 32, 27, 7, 17, 37, 33, 34, 35, 5, 15, 45, 41, 42, 28, 8, 18, 38, 39, 9, 19, 29, 52, 50, 60, 46, 43, 44, 47, 57, 51, 53, 63, 56, 54, 55, 58, 48, 49, 59, 65, 61
OFFSET
1,2
COMMENTS
The 1-digit numbers appear in the sequence in the following order: 0,2,1,3,4,6,7,5,8,9.
After the initial terms, the sequence oscillates about the line y=x.
The first differences are bounded by 30 and -36 for the initial terms, then by 20 and -20. After the first 121 terms the sequence is bounded most of the time by 10 and -10, with eventual jumps that seem to remain bounded by 36 and -36.
LINKS
EXAMPLE
a(2)=10 since it is the smallest number not yet in the sequence that contains the largest digit in a(1)=0; a(3)=20 since it is the smallest number not yet in the sequence that contains the smallest digit in a(2)=10; a(4)=2 since it is the smallest number not yet in the sequence that contains the largest digit in a(3)=20.
MATHEMATICA
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, 72] (* Robert G. Wilson v, Dec 30 2017 *)
CROSSREFS
Cf. A297352.
Sequence in context: A212594 A255529 A023916 * A172503 A107859 A294069
KEYWORD
nonn,base
AUTHOR
Enrique Navarrete, Dec 28 2017
EXTENSIONS
Definition clarified by N. J. A. Sloane, Feb 08 2018
STATUS
approved