A300023 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 9.

9, 10, 20, 30, 21, 1, 2, 3, 13, 40, 41, 4, 5, 50, 42, 6, 12, 60, 22, 7, 11, 70, 14, 16, 80, 8, 32, 61, 19, 81, 29, 71, 15, 17, 18, 23, 24, 52, 51, 39, 62, 28, 72, 38, 63, 27, 73, 37, 64, 26, 74, 36, 65, 25, 75, 31, 33, 34, 47, 53, 57, 43, 67, 35, 45, 54, 46, 55, 85, 90, 100, 110, 44, 48, 58, 66

Offset

1,1

Comments

The sequence starts with a(1) = 9 and is always extended with the smallest integer not yet present that does not lead to a contradiction.

A permutation of the natural numbers.

Links

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

Example

9 shows a digit 9, of course (k = 1)
9 + 10 = 19 and 19 shows at least a digit 9 (k = 2)
9 + 10 + 20 = 39 and 39 shows at least a digit 9 (k = 3)
9 + 10 + 20 + 30 = 69 and 69 shows at least a digit 9 (k = 4)
9 + 10 + 20 + 30 + 21 = 90 and 90 shows at least a digit 9 (k = 5)
9 + 10 + 20 + 30 + 21 + 1 = 91 and 91 shows at least a digit 9 (k = 6)
...

Crossrefs

Cf. A300015 (which is the lexicographic first sequence of positive integers without duplicate terms having this property).

Sequence in context: A182396 A041162 A041691 * A022314 A178350 A085949

Adjacent sequences: A300020 A300021 A300022 * A300024 A300025 A300026

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

Status

approved