A316915 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shares at least two digits with a(k). Lexicographic first sequence of positive integers without duplicate terms having this property.

10, 100, 11, 13, 14, 16, 18, 20, 12, 23, 26, 29, 32, 35, 39, 24, 46, 51, 45, 40, 67, 74, 27, 19, 21, 90, 101, 30, 41, 106, 15, 61, 17, 31, 33, 37, 84, 50, 56, 62, 69, 47, 81, 91, 102, 60, 71, 92, 22, 28, 112, 34, 42, 25, 52, 117, 72, 82, 38, 95, 80, 103, 43, 73, 133, 36, 93, 53, 63, 70, 78, 83, 59, 49, 104

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 16 2018

Keywords

• base
• nonn

Examples

			Here are the first terms of the sequence:
10,100,11,13,14,16,18,20,12,23,26,29,32,...
and here are the cumulative sums:
10,110,121,134,148,162,180,200,212,235,261,290,322,...
If we align a(n) and its cumulative sum, we see that at least two digits are shared:
  10,100, 11, 13, 14, 16, 18, 20, 12, 23, 26, 29, 32,...
  10,110,121,134,148,162,180,200,212,235,261,290,322,...
		

Links

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

Crossrefs

Cf. A316914 (where one digit is shared instead of two, by the cumulative sum).