A302799 Lexicographically earliest sequence of distinct terms such that adding 10 to each term produces a new sequence that has exactly the same succession of digits as the present one.

1, 12, 2, 121, 3, 11, 32, 14, 22, 4, 321, 43, 31, 5, 34, 115, 44, 125, 54, 13, 56, 42, 36, 6, 52, 46, 16, 62, 562, 67, 25, 7, 27, 73, 51, 737, 8, 361, 74, 71, 83, 718, 48, 19, 37, 28, 58, 29, 47, 38, 68, 39, 57, 487, 84, 9, 674, 97, 94, 196, 8410, 710, 420, 684, 20, 720, 430, 69, 4307, 30

Offset: 1

Author

Eric Angelini and Hans Havermann, Apr 13 2018

Keywords

• nonn
• base

Comments

The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.

Examples

			    1 = a(1) is replaced by   1 + 10 =  11
   12 = a(2) is replaced by  12 + 10 =  22
    2 = a(3) is replaced by   2 + 10 =  12
  121 = a(4) is replaced by 121 + 10 = 131
    3 = a(5) is replaced by   3 + 10 =  13
   11 = a(6) is replaced by  11 + 10 =  21
   32 = a(7) is replaced by  32 + 10 =  42
   14 = a(8) is replaced by  14 + 10 =  24
etc.
We see that the first and the last column here (which are respectively the terms of the present sequence and the terms of the transformed one) share the same succession of digits (so far): 1,1,2,2,1,2,1,3,1,1,3,2,1,4,2,2,4,...
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..1000
• Hans Havermann, Graph of the first 100000 terms

Crossrefs

Cf. A302656 for another transformation in the same spirit that preserves the succession of digits in the sequence.