Fw: zeroless squares

[wouter meeussen]

blushing, I meekly forward

W.
----- Original Message -----
From: "Ron" <ron at ronknott.com>
To: "wouter meeussen" <wouter.meeussen at pandora.be>
Sent: Saturday, February 26, 2005 7:47 PM
Subject: zeroless squares


This is not correct:  there are three squares with 1 digit: 1, 4, 9, not
2 and 19 not 18 with 3 digits.
  I tried to send this to seqfan but it seems to be ignoring any message
I send it at present
   The Maple code I used is:

   seq(
      sum('`if`( searchtext("0",convert(i^2,string))>0 , 0, 1 )',
      'i'=ceil(10^(n/2))..floor(10^((n+1)/2))
         ),
       n=0..2);
Ron Knott


> Table[Count[Range[Ceiling[ 10^(k/2)] , Floor[ -1 + 10^(k/2 + 1/2)
]]^2,
>     q_Integer /; DigitCount[q, 10, 0] === 0], {k, 0, 12}]
>
> gives
> {2, 6, 18, 44, 135, 376, 1060, 2985, 8431, 24009, 67982, 193359,
549696}
>
> I am sorry, but the terms
> 2, 6, 18, 44, 135, 376, 1060, 2985, 8431
> do not match anything in the table
>
> W.
>
>
>
> ----- Original Message -----
> From: "N. J. A. Sloane" <njas at research.att.com>
> To: <seqfan at ext.jussieu.fr>
> Cc: <rcs at cs.arizona.edu>
> Sent: Saturday, February 26, 2005 6:37 PM
> Subject: zeroless squares / will be away
>
>
> 1. A recent message from Richard Schroeppel has drawn attention to
> the question: Are there infinitely many squares with all digits not
> zero?
> The sequence is A052041.
> It might be interesting to see the sequence
> a(n) = number of n-digit squares with no zero digits
> , if someone would care to work it out.
>
> Richard asks in particular, can one find an explicit infinite
> sequence of squares with no zero digits?  E.g. can one generalize
> 6666^2 = 44435556 ?
>
> 2. I will be traveling Mar 2 - 7, no updates during that period.
> But all messages will be saved.  There are still 200 Comments
> waiting to be processed, and I may not
> get caught up until the middle of March.
>
> NJAS
>
>
>