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.

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

Robert G. Wilson v, Table of n, a(n) for n = 1..5000

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

Adjacent sequences: A297350 A297351 A297352 * A297354 A297355 A297356

Keyword

nonn,base

Author

Enrique Navarrete, Dec 28 2017

Extensions

Definition clarified by N. J. A. Sloane, Feb 08 2018

Status

approved