A300016 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 2.

2, 10, 8, 1, 3, 4, 14, 20, 30, 28, 5, 7, 40, 29, 6, 9, 11, 12, 13, 15, 16, 19, 18, 22, 50, 31, 39, 58, 32, 60, 17, 23, 68, 42, 59, 21, 70, 80, 33, 27, 69, 41, 38, 24, 25, 26, 37, 90, 100, 110, 108, 52, 48, 62, 43, 47, 34, 35, 36, 44, 45, 46, 49, 51, 53, 54, 55, 56, 57, 61, 63, 64, 65, 66, 67

Offset

1,1

Comments

The sequence starts with a(1) = 2 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

2 shows a digit 2, of course (k = 1)
2 + 10 = 12 and 12 shows at least a digit 2 (k = 2)
2 + 10 + 8 = 20 and 20 shows at least a digit 2 (k = 3)
2 + 10 + 8 + 1 = 21 and 21 shows at least a digit 2 (k = 4)
2 + 10 + 8 + 1 + 3 = 24 and 24 shows at least a digit 2 (k = 5)
2 + 10 + 8 + 1 + 3 + 4 = 28 and 28 shows at least a digit 2 (k = 6)
...

Crossrefs

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

Sequence in context: A248061 A267500 A355785 * A368559 A166542 A316967

Adjacent sequences: A300013 A300014 A300015 * A300017 A300018 A300019

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

Status

approved