A326639 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shares at least four digits with a(k). Lexicographically first sequence of positive integers without duplicate terms having this property.

1000, 10000, 1001, 1003, 1004, 1035, 1061, 1127, 1184, 1095, 1200, 2300, 2050, 2370, 1280, 1300, 1030, 3040, 1530, 3950, 4390, 4080, 5030, 1040, 6000, 1600, 3600, 7200, 2700, 8300, 3800, 1800, 1002, 1129, 1936, 1649, 1296, 1799, 1090, 1010, 1012, 1020, 1038, 1008, 1005, 1006, 1007, 1011, 1013, 1014, 1105, 1120, 1031

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 15 2019

Keywords

• base
• nonn

Examples

			Here are the first terms of the sequence:
1000,10000,1001,1003,1004,1035,1061,1127,1184,...
and here are the cumulative sums:
1000,11000,12001,13004,14008,15043,16104,17231,18415,...
If we align a(n) and its cumulative sum, we see that at least four digits are shared:
1000,10000, 1001, 1003, 1004, 1035 ,1061, 1127, 1184,...
1000,11000,12001,13004,14008,15043,16104,17231,18415,...
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..5001

Crossrefs

Cf. A309151 (no digit is shared by the cumulative sum instead of four digits here), A316914 (one digit is shared), A316915 (two digits shared), A326638 (three digits shared), A326640 (five digits shared).