Intended for: October 11, 2012
Timetable
- First draft entered by Alonso del Arte on July 10, 2011 ✓
- Draft reviewed by Mitch Harris on August 9, 2011 ✓
- Draft reviewed by M. F. Hasler on October 10, 2012 ✓
- Draft approved by Daniel Forgues on October 10, 2012, October 8, 2016 ✓
The line below marks the end of the <noinclude> ... </noinclude> section.
A001020:
-
{ 1, 11, 121, 1331, 14641, 161051, ... }
The decimal digits of the powers of 11 give binomial coefficients (which appear in Pascal’s triangle), until some binomial coefficients have more than one digit, where overlapping occurs.
Pascal’s triangle
|
|
0
|
|
1
|
|
1
|
|
1
|
1
|
|
2
|
|
1
|
2
|
1
|
|
3
|
|
1
|
3
|
3
|
1
|
|
4
|
|
1
|
4
|
6
|
4
|
1
|
|
5
|
|
1
|
5
|
10
|
10
|
5
|
1
|
|
|
|
|
1
|
2
|
3
|
4
|
5
|
|
|
After 11 4 it doesn’t quite work out, since some binomial coefficients in {1, 5, 10, 10, 5, 1} have more than one decimal digits.
1,
5,
1 0,
1 0,
5,
1
----------------
1 6 1 0 5 1
In fact, the powers of 11 correspond to a Pascal’s triangle with only one digit per entry, and carry over to the next cell to the left in case of a value ≥ 10.
In general, if
appears in Pascal’s triangle in the middle of row
, then
can be found in Pascal’s triangle written in base
up to
.