 | 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 |
Gelfand's question concerns the leftmost (i.e., most significant) decimal digit of the powers 
, 
, ..., 
. The patterns of digits in the
table for 
,
2, ... lead to the following questions (King 1994).
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 
? It does not recur, so its natural
density is 0 (Eising et al. 2015, pp. 236 and 238-239).
3. Will a row of all the same digit occur? No, for any positive integer 
(Eising et al. 2015, pp. 236 and 239).
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).
For each base separately, the problem of leading digits corresponds to an irrational rotation of a circle. King (1994, pp. 619-624) relates this dynamical system to the circle map arising in Poncelet's porism.
