A300022 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 8.

8, 10, 20, 30, 12, 1, 2, 3, 22, 40, 32, 4, 5, 9, 50, 33, 6, 11, 60, 23, 7, 70, 24, 16, 80, 90, 13, 17, 82, 18, 14, 15, 19, 21, 25, 26, 62, 28, 72, 38, 63, 27, 73, 37, 64, 36, 65, 35, 66, 34, 67, 43, 52, 29, 31, 39, 49, 53, 47, 54, 46, 55, 45, 56, 44, 57, 83, 100, 110, 102, 41, 42, 75, 48, 92

Offset

1,1

Comments

The sequence starts with a(1) = 8 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

8 shows a digit 8, of course (k = 1)
8 + 10 = 18 and 18 shows at least a digit 8 (k = 2)
8 + 10 + 20 = 38 and 38 shows at least a digit 8 (k = 3)
8 + 10 + 20 + 30 = 68 and 68 shows at least a digit 8 (k = 4)
8 + 10 + 20 + 30 + 12 = 80 and 80 shows at least a digit 8 (k = 5)
8 + 10 + 20 + 30 + 12 + 1 = 81 and 81 shows at least a digit 8 (k = 6)
...

Crossrefs

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

Sequence in context: A230862 A281067 A070974 * A346783 A073619 A338820

Adjacent sequences: A300019 A300020 A300021 * A300023 A300024 A300025

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

Status

approved