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

1,1

Links

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

Example

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,...

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).

Sequence in context: A019548 A017271 A017511 * A017643 A161770 A004632

Adjacent sequences: A326636 A326637 A326638 * A326640 A326641 A326642

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Jul 15 2019

Status

approved