A316914 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shares at least one digit of a(k). Lexicographic first sequence of positive integers without duplicate terms having this property.

1, 10, 12, 2, 13, 4, 15, 6, 7, 3, 8, 9, 5, 11, 14, 16, 17, 18, 19, 20, 21, 22, 23, 26, 24, 25, 27, 30, 31, 34, 29, 32, 28, 35, 33, 36, 37, 40, 38, 42, 41, 39, 43, 48, 46, 44, 51, 49, 52, 59, 45, 47, 54, 60, 50, 56, 58, 57, 53, 61, 69, 62, 63, 55, 64, 67, 68, 72, 71, 70, 65, 66, 73, 74, 75

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 16 2018

Keywords

• base
• nonn

Examples

			Here are the first terms of the sequence:
1,10,12,2,13,4,15,6,7,3,8,9,5,11,14,16,...
and here are the cumulative sums:
1,11,23,25,38,42,57,63,70,73,81,90,95,106,120,136,...
If we align a(n) and its cumulative sum, we see that at least one digit is shared:
1,10,12, 2,13, 4,15, 6, 7, 3, 8, 9, 5, 11, 14, 16,...
1,11,23,25,38,42,57,63,70,73,81,90,95,106,120,136,...
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001