Re zeroless squares

[N. J. A. Sloane]

My apologies to Richard Schroeppel!   I misread his original message.

Here is what he said:

> Is there a parametric set of 0-less squares?   777...444 seems to fail.
> 
> 9999^2 = 99980001.  Divide by 9 to get 3333^2 = 11108889.  Close, but no cigar.
> Multiply by 4 to get 6666^2 = 44435556.  Bingo.
> 
> Is there any way to find 0-less powers other than scanning for them?
> Presumably the 0-less squares thin out but never completely disappear.
> It might be possible to use stats to prove density upper bounds on 0-less
> squares or powers of 2.

and as Ignacio Larrosa Ca<F1>estro points out:

> A(k) = 6[k] = 6(10^k - 1)/9  ===>

> (A(k))^2 = (6(10^k-1)/9)^2 = (4/9)(10^(2k) - 2*10^k + 1)

> which is k-1 4's, followed by a 3, k-1 5's and a 6.

So I will add this

%S A102794 1,36,4356,443556,44435556,4444355556,444443555556,44444435555556,4444444355555556,
%T A102794 444444443555555556,44444444435555555556,4444444444355555555556,444444444443555555555556,
%U A102794 44444444444435555555555556,4444444444444355555555555556,444444444444443555555555555556
%N A102794 The number (666...6)^2.
%C A102794 An infinite sequence of squares with no zeros in base 10.
...

as a new sequence.

NJAS