A297352 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.

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

Offset

1,2

Comments

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

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..11111

Example

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.

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, 70] (* Robert G. Wilson v, Dec 29 2017 *)

Crossrefs

Cf. A297353.

Sequence in context: A239113 A107353 A297418 * A370401 A172171 A327723

Adjacent sequences: A297349 A297350 A297351 * A297353 A297354 A297355

Keyword

nonn,base

Author

Enrique Navarrete, Dec 28 2017

Extensions

Corrected a(65) onward by Robert G. Wilson v, Dec 29 2017

Definition clarified by N. J. A. Sloane, Jan 19 2018 and again Feb 08 2018

Status

approved