|
%I #21 Feb 19 2019 14:41:50
%S 1,9,2,3,4,12,10,20,30,11,5,6,7,8,13,14,15,16,24,21,40,39,31,50,19,41,
%T 59,51,49,61,42,18,60,22,28,69,71,23,17,25,26,27,29,32,33,34,35,36,37,
%U 38,43,44,45,46,47,48,52,53,54,55,56,57,58,70,62,68,79,81,80,90,100,110,120,119
%N For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 1. Lexicographic first sequence of positive integers without duplicate terms having this property.
%C The sequence starts with a(1) = 1 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.
%C A fractal structure arises when considering the sequence b defined by b(n) = a(n) - n at different scales. - _Rémy Sigrist_, Feb 19 2019
%H Jean-Marc Falcoz, <a href="/A300015/b300015.txt">Table of n, a(n) for n = 1..10001</a>
%H Rémy Sigrist, <a href="/A300015/a300015.png">Scatterplot of (n, a(n)-n) for n = 1..1000000</a>
%e 1 shows a digit 1, of course (k = 1)
%e 1 + 9 = 10 and 10 shows at least a digit 1 (k = 2)
%e 1 + 9 + 2 = 12 and 12 shows at least a digit 1 (k = 3)
%e 1 + 9 + 2 + 3 = 15 and 15 shows at least a digit 1 (k = 4)
%e 1 + 9 + 2 + 3 + 4 = 19 and 19 shows at least a digit 1 (k = 5)
%e 1 + 9 + 2 + 3 + 4 + 12 = 31 and 31 shows at least a digit 1 (k = 6)
%e ...
%Y Cf. A300021.
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 23 2018
|
