

A300015


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.


10



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, 59, 51, 49, 61, 42, 18, 60, 22, 28, 69, 71, 23, 17, 25, 26, 27, 29, 32, 33, 34, 35, 36, 37, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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.
A permutation of the natural numbers.
A fractal structure arises when considering the sequence b defined by b(n) = a(n)  n at different scales.  Rémy Sigrist, Feb 19 2019


LINKS



EXAMPLE

1 shows a digit 1, of course (k = 1)
1 + 9 = 10 and 10 shows at least a digit 1 (k = 2)
1 + 9 + 2 = 12 and 12 shows at least a digit 1 (k = 3)
1 + 9 + 2 + 3 = 15 and 15 shows at least a digit 1 (k = 4)
1 + 9 + 2 + 3 + 4 = 19 and 19 shows at least a digit 1 (k = 5)
1 + 9 + 2 + 3 + 4 + 12 = 31 and 31 shows at least a digit 1 (k = 6)
...


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



