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

1,1

Links

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

Example

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,...

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).

Sequence in context: A030024 A232657 A287027 * A284515 A068086 A115691

Adjacent sequences: A326635 A326636 A326637 * A326639 A326640 A326641

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Jul 15 2019

Status

approved