A326639 - OEIS

%I #10 Dec 06 2019 21:45:32

%S 1000,10000,1001,1003,1004,1035,1061,1127,1184,1095,1200,2300,2050,

%T 2370,1280,1300,1030,3040,1530,3950,4390,4080,5030,1040,6000,1600,

%U 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

%N 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.

%H Jean-Marc Falcoz, <a href="/A326639/b326639.txt">Table of n, a(n) for n = 1..5001</a>

%e Here are the first terms of the sequence:

%e 1000,10000,1001,1003,1004,1035,1061,1127,1184,...

%e and here are the cumulative sums:

%e 1000,11000,12001,13004,14008,15043,16104,17231,18415,...

%e If we align a(n) and its cumulative sum, we see that at least four digits are shared:

%e 1000,10000, 1001, 1003, 1004, 1035 ,1061, 1127, 1184,...

%e 1000,11000,12001,13004,14008,15043,16104,17231,18415,...

%Y 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).

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 15 2019