|
|
A300023
|
|
For any k, the cumulative sum a(1) + a(2) + a(3) + ... + a(k) shows at least a digit 9.
|
|
1
|
|
|
9, 10, 20, 30, 21, 1, 2, 3, 13, 40, 41, 4, 5, 50, 42, 6, 12, 60, 22, 7, 11, 70, 14, 16, 80, 8, 32, 61, 19, 81, 29, 71, 15, 17, 18, 23, 24, 52, 51, 39, 62, 28, 72, 38, 63, 27, 73, 37, 64, 26, 74, 36, 65, 25, 75, 31, 33, 34, 47, 53, 57, 43, 67, 35, 45, 54, 46, 55, 85, 90, 100, 110, 44, 48, 58, 66
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The sequence starts with a(1) = 9 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
|
|
|
EXAMPLE
|
9 shows a digit 9, of course (k = 1)
9 + 10 = 19 and 19 shows at least a digit 9 (k = 2)
9 + 10 + 20 = 39 and 39 shows at least a digit 9 (k = 3)
9 + 10 + 20 + 30 = 69 and 69 shows at least a digit 9 (k = 4)
9 + 10 + 20 + 30 + 21 = 90 and 90 shows at least a digit 9 (k = 5)
9 + 10 + 20 + 30 + 21 + 1 = 91 and 91 shows at least a digit 9 (k = 6)
...
|
|
CROSSREFS
|
Cf. A300015 (which is the lexicographic first sequence of positive integers without duplicate terms having this property).
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|