zeroless squares

[Pfoertner, Hugo]

-----Original Message-----
From: Pfoertner, Hugo [mailto:Hugo.Pfoertner at muc.mtu.de] 
Sent: Monday, February 28, 2005 08:39
To: seqfan at ext.jussieu.fr
Subject: RE: zeroless squares

This suggests a new sequence:

Smallest power with base>1, exponent>1 whose decimal representation doesn't
contain the digit 0:

base exponent                base^exponent

more terms:

 2  1                                    2
 2  2                                    4
 2  3                                    8
 2  4                                   16
 2  5                                   32
 2  6                                   64
 2  7                                  128
 2  8                                  256
 2  9                                  512
 5 10                              9765625
 3 11                               177147
 3 12                               531441
 2 13                                 8192
 2 14                                16384
 2 15                                32768
 2 16                                65536
 4 17                          17179869184
 2 18                               262144
 2 19                               524288
12 20               3833759992447475122176
22 22       341427877364219557396646723584
 3 23                          94143178827
 2 24                             16777216
 2 25                             33554432
 3 26                        2541865828329
 2 27                            134217728
 2 28                            268435456
 6 29              36845653286788892983296
 5 30                931322574615478515625
 2 31                           2147483648
 2 32                           4294967296
 2 33                           8589934592
 2 34                          17179869184
 2 35                          34359738368
 2 36                          68719476736
 2 37                         137438953472
 4 38              75557863725914323419136
 2 39                         549755813888

x^40 exceeds 33 decimal digits.

Hugo