A326638 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shares at least three digits with a(k). Lexicographically first sequence of positive integers without duplicate terms having this property.

100, 1000, 101, 103, 104, 135, 171, 128, 119, 120, 109, 121, 256, 147, 239, 163, 304, 370, 340, 450, 240, 200, 150, 250, 600, 160, 130, 700, 170, 131, 812, 380, 168, 693, 379, 300, 110, 102, 106, 151, 167, 107, 108, 140, 111, 105, 112, 114, 115, 117, 118, 113, 126, 129, 123, 124, 125, 137, 122, 149

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 15 2019

Keywords

• base
• nonn

Examples

			Here are the first terms of the sequence:
100,1000,101,103,104,135,171,128,119,120,...
and here are the cumulative sums:
100,1100,1201,1304,1408,1543,1714,1842,1961,2081,...
If we align a(n) and its cumulative sum, we see that at least three digits are shared:
  100,1000, 101, 103, 104 ,135, 171, 128, 119, 120,...
  100,1100,1201,1304,1408,1543,1714,1842,1961,2081,...
		

Links

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

Crossrefs

Cf. A309151 (where no digit is shared by the cumulative sum), A316914 (where one digit is shared instead of three, by the cumulative sum), A316915 (two digits shared), A326639 (four digits shared), A326640 (five digits shared).