A300015 - OEIS

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.

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

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Rémy Sigrist, Scatterplot of (n, a(n)-n) for n = 1..1000000

EXAMPLE

1 shows a digit 1, of course (k = 1)