A300021 - OEIS

%I #8 Feb 23 2018 22:17:06

%S 7,10,20,30,3,1,2,4,40,50,5,6,9,60,23,8,19,70,11,29,63,17,80,12,18,73,

%T 27,13,14,15,16,21,22,39,33,37,64,26,74,36,65,25,75,35,66,24,76,34,67,

%U 43,53,31,28,32,38,48,90,41,49,44,46,54,56,45,55,47,83,100,110,42,51,57,58,52,120,123,77,124,86,113,87,59,61,93,97,103,101,96,104,99,102

%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 7.

%C The sequence starts with a(1) = 7 and is always extended with the smallest integer not yet present that does not lead to a contradiction.

%C A permutation of the natural numbers.

%H Jean-Marc Falcoz, <a href="/A300021/b300021.txt">Table of n, a(n) for n = 1..10001</a>

%e 7 shows a digit 7, of course (k = 1)

%e 7 + 10 = 17 and 17 shows at least a digit 7 (k = 2)

%e 7 + 10 + 20 = 37 and 37 shows at least a digit 7 (k = 3)

%e 7 + 10 + 20 + 30 = 67 and 67 shows at least a digit 7 (k = 4)

%e 7 + 10 + 20 + 30 + 3 = 70 and 70 shows at least a digit 7 (k = 5)

%e 7 + 10 + 20 + 30 + 3 + 1 = 71 and 71 shows at least a digit 7 (k = 6)

%e ...

%Y Cf. A300015 (which is the lexicographic first sequence of positive integers without duplicate terms having this property).

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 23 2018