A286890 a(n) is the least positive integer not yet in the sequence that shares its largest digit with that of a(n-1); a(1)=1.

1, 10, 11, 12, 2, 20, 21, 22, 23, 3, 13, 30, 31, 32, 33, 34, 4, 14, 24, 40, 41, 42, 43, 44, 45, 5, 15, 25, 35, 50, 51, 52, 53, 54, 55, 56, 6, 16, 26, 36, 46, 60, 61, 62, 63, 64, 65, 66, 67, 7, 17, 27, 37, 47, 57, 70, 71, 72, 73, 74, 75, 76, 77, 78, 8, 18, 28, 38, 48, 58, 68, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 19, 29, 39, 49, 59, 69, 79, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 119, 129

Offset: 1

Author

Enrique Navarrete, Jul 22 2017

Keywords

• nonn
• base

Comments

After a(81) = 89, each term must contain a 9.

Unlike A184992, not a permutation of the positive integers, but contains all numbers from 1 to 99.

Examples

			Gathering intervals of consecutive integers, sequence begins as follows:
1,                               10..12,
2,                               20..23,
3, 13,                           30..34,
4, 14, 24,                       40..45,
5, 15, 25, 35,                   50..56,
6, 16, 26, 36, 46,               60..67,
7, 17, 27, 37, 47, 57,           70..78,
8, 18, 28, 38, 48, 58, 68,       80..89,
9, 19, 29, 39, 49, 59, 69, 79,   90..99,
109, 119, 129, ...
		

Links

• Jean-Marc Falcoz and Eric Angelini, Table of n, a(n) for n = 1..5001

Crossrefs

Cf. A184992.

Programs

Mathematica

a = {1}; Do[k = 2; While[Nand[! MemberQ[a, k], MemberQ[IntegerDigits[k], Max@ IntegerDigits[a[[n - 1]] ]]], k++]; AppendTo[a, k], {n, 2, 102}]; a (* Michael De Vlieger, Jul 22 2017 *)