A300018 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 4.

4, 10, 20, 6, 1, 2, 3, 8, 30, 40, 16, 5, 9, 50, 36, 7, 17, 60, 18, 12, 46, 11, 13, 14, 15, 19, 21, 31, 22, 28, 66, 24, 70, 80, 26, 34, 67, 23, 76, 44, 56, 54, 47, 33, 68, 32, 27, 25, 29, 35, 51, 43, 57, 53, 48, 42, 58, 52, 49, 41, 59, 61, 37, 63, 38, 62, 39, 64, 45, 72, 90, 100, 110, 116, 74

Offset

1,1

Comments

The sequence starts with a(1) = 4 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

4 shows a digit 4, of course (k = 1)
4 + 10 = 14 and 14 shows at least a digit 4 (k = 2)
4 + 10 + 20 = 34 and 34 shows at least a digit 4 (k = 3)
4 + 10 + 20 + 6 = 40 and 40 shows at least a digit 4 (k = 4)
4 + 10 + 20 + 6 + 1 = 41 and 41 shows at least a digit 4 (k = 5)
4 + 10 + 20 + 6 + 1 + 2 = 43 and 43 shows at least a digit 4 (k = 6)
...

Crossrefs

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

Sequence in context: A155383 A155229 A155220 * A268221 A086176 A015789

Adjacent sequences: A300015 A300016 A300017 * A300019 A300020 A300021

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

Status

approved