A362987 Lexicographically earliest sequence S of distinct positive terms such that the successive digits of S are the successive spreads of S' terms (see Comments for definition of "spread").

10, 11, 12, 21, 23, 13, 20, 32, 24, 14, 34, 25, 31, 22, 30, 35, 42, 15, 43, 26, 36, 37, 46, 16, 41, 45, 53, 57, 47, 33, 52, 27, 40, 64, 54, 38, 48, 58, 68, 17, 63, 28, 69, 18, 51, 39, 56, 60, 59, 65, 62, 49, 50, 74, 61, 29, 73, 70, 85, 96, 72, 75, 79, 81, 84, 44, 71, 95, 83, 105, 104, 19

Offset: 1

Author

Eric Angelini, May 12 2023

Keywords

• base
• nonn

Comments

The spread of n is the absolute difference between the leftmost digit of n and the rightmost digit of n. Spreads vary from 0 to 9.

Examples

			a(1) = 10 with spread 1;
a(2) = 11 with spread 0;
a(3) = 12 with spread 1;
a(4) = 21 with spread 1;
a(5) = 23 with spread 1;
a(6) = 13 with spread 2; etc.
We see that the above succession of spreads is the digits' succession of S.
		

Crossrefs

Cf. A100787.

Programs

Mathematica

a[1]=10;a[n_]:=a[n]=Block[{k=10},While[Abs[First@#-Last@#]&@IntegerDigits[k][[{1,-1}]]!=Flatten[IntegerDigits/@Array[a,n-1]][[n]]||MemberQ[Array[a,n-1],k],k++];k];Array[a,72] (* Giorgos Kalogeropoulos, May 12 2023 *)