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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

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)

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

Cf. A300021.

Sequence in context: A222226 A104539 A201559 * A246499 A199002 A160108

Adjacent sequences:  A300012 A300013 A300014 * A300016 A300017 A300018

KEYWORD

nonn,base

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

STATUS

approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)