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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
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.
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
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Hans Havermann, Apr 13 2018
STATUS
approved