 | Sloane's |  |  |  |  |  |  |  |  |
| 1 | A000027 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 2 | A002993 | 4 | 9 | 1 | 2 | 3 | 4 | 6 | 8 |
| 3 | A002994 | 8 | 2 | 6 | 1 | 2 | 3 | 5 | 7 |
| 4 | A097408 | 1 | 8 | 2 | 6 | 1 | 2 | 4 | 6 |
| 5 | A097409 | 3 | 2 | 1 | 3 | 7 | 1 | 3 | 5 |
| 6 | A097410 | 6 | 7 | 4 | 1 | 4 | 1 | 2 | 5 |
| 7 | A097411 | 1 | 2 | 1 | 7 | 2 | 8 | 2 | 4 |
| 8 | A097412 | 2 | 6 | 6 | 3 | 1 | 5 | 1 | 4 |
| 9 | A097413 | 5 | 1 | 2 | 1 | 1 | 4 | 1 | 3 |
| 10 | A097414 | 1 | 5 | 1 | 9 | 6 | 2 | 1 | 3 |
Consider the leftmost (i.e., most significant) decimal digit of the numbers 
, 
, ..., 
. Then what are the patterns of digits occurring in the table
for 
,
2, ... (King 1994)? For example,
1. Will the digit 9 ever occur in the 
column? The answer is "yes," in particular at
values 
,
63, 73, 83, 93, 156, 166, 176, ... (OEIS A097415.
This problem appears in Avez (1966, p. 37), where it is attributed to Gelfand.
2. Will the row "23456789" ever appear for 
? None does for 
. If so, will it have a frequency? If so, will the
frequency be rational or irrational?
3. Will a row of all the same digit occur? No such example occurs for 
.
4. Will the decimal expansion of an 8-digit prime ever occur? (The answer is "yes," in particular at values 
, 11, 21, 44, 55, 81, 90, 118, 126, ... (OEIS A097616),
corresponding to the primes 23456789, 21443183, 21442591, 19351159, ... (OEIS A097617).
Amazingly, this problem is isomorphic to Poncelet's porism (King 1994).
