A109638 A monotonic sequence obeying a different 10-digit rule than A101246.

1, 3, 7, 12, 18, 27, 37, 38, 40, 45, 51, 60, 61, 63, 67, 72, 80, 89, 90, 92, 95, 99, 105, 112, 115, 125, 132, 140, 149, 151, 154, 160, 167, 175, 184, 186, 189, 194, 271, 281, 284, 289, 295, 302, 303

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Example

Superimpose sequence and first differences:
Sequence.......: 1 3 7 12 18 27 37 38 40 45 51 60 61 63 67 72 80 89 90
First differences: .2.4.5..6..9..10.1..2..5..6..9..1..2..4..5..8..9..1..
Start with a(1)=1
+ add 2 [which is the smallest integer containing a digit not yet present in the sequence or in the first differences (0 cannot be added as the sequence is monotonic)]:
= we get a(2)=3;
+ add 4 [which is the smallest integer containing a digit not yet present in the sequence or in the first differences]:
= we get a(3)=7
+ add 5 [...]
= we get a(4)=12
+ add 6
= a(5)=18
+ add 9
= a(6)=27
+ add 10
= a(7)=37
We have used now all 10 digits, either in the sequence itself, or in the first differences. Let's introduce the "10-digit chunk" notion:
- the first "10-digit chunk" starts with a(1) and stops immediately after the last of the ten digits we had to include: so the first chunk is made by the (virtual) succession of [1,2,3,4,7,5,12,6,18,9,27,10];
- the second chunk is [37,1,38,2,40,5,45,6,51,9];
- the third chunk is [60,1,61,2,63,4,67,5,72,8,80,9];
- the fourth chunk is [89,1,90,2,92,3,95,4,99,6,105,7];
- ...
- the eighth chunk is [281,3,284,5,289,6,295,7,30]2 (yes, a chunk ends sometimes in the middle of a(n), here a(n)=302 -- thus the next chunk will also start in the middle of that a(n): [2,1,303...])
- etc.

Crossrefs

Sequence in context: A169679 A024388 A184534 * A008332 A065390 A171835

Adjacent sequences: A109635 A109636 A109637 * A109639 A109640 A109641

Keyword

base,easy,nonn

Author

Eric Angelini, Aug 30 2005

Status

approved