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