zeroless squares / will be away

[Ignacio Larrosa Cañestro]

Saturday, February 26, 2005 6:37 PM [GMT+1=CET],
N. J. A. Sloane <njas at research.att.com> escribió:

> 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 ?
>

But it is inmediate:

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

    = (4/9)(10^(2k) - 1) - (8/9)(10^(k) - 1)

   = 4[k-1]35[k-1]6

Its says, k-1 4's, followed by a 3, k-1 5's and a 6.

Best regards,

Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosa at mundo-r.com