A300024 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 0.

10, 20, 30, 40, 1, 2, 3, 4, 50, 41, 5, 14, 60, 21, 6, 13, 70, 11, 7, 12, 80, 8, 22, 71, 9, 90, 100, 101, 19, 81, 15, 16, 17, 18, 23, 110, 102, 28, 72, 38, 61, 29, 73, 27, 74, 26, 75, 25, 76, 24, 77, 31, 32, 33, 37, 62, 48, 51, 39, 63, 47, 52, 58, 42, 68, 34, 36, 64, 46, 53, 57, 43, 35, 44, 78

Offset

1,1

Comments

The sequence starts with a(1) = 10 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

10 shows at least a digit 0, of course (k = 1)
10 + 20 = 30 and 30 shows at least a digit 0 (k = 2)
10 + 20 + 30 = 60 and 60 shows at least a digit 0 (k = 3)
10 + 20 + 30 + 40 = 100 and 100 shows at least a digit 0 (k = 4)
10 + 20 + 30 + 40 + 1 = 101 and 101 shows at least a digit 0 (k = 5)
10 + 20 + 30 + 40 + 1 + 2 = 103 and 103 shows at least a digit 0 (k = 6)
...

Crossrefs

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

Sequence in context: A095208 A291625 A172260 * A069534 A237416 A236507

Adjacent sequences: A300021 A300022 A300023 * A300025 A300026 A300027

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

Status

approved