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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
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified June 20 23:18 EDT 2024. Contains 373535 sequences. (Running on oeis4.)