A300017 For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 3.

3, 10, 17, 1, 2, 4, 6, 20, 30, 37, 5, 8, 40, 47, 7, 16, 48, 9, 11, 12, 13, 14, 15, 18, 38, 22, 50, 27, 23, 60, 19, 21, 70, 80, 28, 32, 67, 33, 68, 42, 57, 43, 58, 52, 24, 25, 26, 29, 36, 90, 100, 110, 107, 53, 49, 31, 69, 41, 59, 51, 54, 46, 34, 35, 39, 44, 78, 117, 63, 45, 55, 120, 87, 56, 61

Offset

1,1

Comments

The sequence starts with a(1) = 3 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

3 shows a digit 3, of course (k = 1)
3 + 10 = 13 and 13 shows at least a digit 3 (k = 2)
3 + 10 + 17 = 30 and 30 shows at least a digit 3 (k = 3)
3 + 10 + 17 + 1 = 31 and 31 shows at least a digit 3 (k = 4)
3 + 10 + 17 + 1 + 2 = 33 and 33 shows at least a digit 3 (k = 5)
3 + 10 + 17 + 1 + 2 + 4 = 37 and 37 shows at least a digit 3 (k = 6)
...

Crossrefs

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

Sequence in context: A366395 A059911 A160375 * A176760 A188396 A356090

Adjacent sequences: A300014 A300015 A300016 * A300018 A300019 A300020

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 23 2018

Status

approved