zeroless squares / will be away

[wouter meeussen]

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