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

1,2

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.

Links

Hans Havermann, Table of n, a(n) for n = 1..1000

Hans Havermann, Graph of the first 100000 terms

Example

    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,...

Crossrefs

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

Sequence in context: A040143 A163599 A334700 * A213059 A038328 A126860

Adjacent sequences: A302796 A302797 A302798 * A302800 A302801 A302802

Keyword

nonn,base

Author

Eric Angelini and Hans Havermann, Apr 13 2018

Status

approved