zeroless squares / will be away

[Ignacio Larrosa Cañestro]

Saturday, February 26, 2005 7:27 PM [GMT+1=CET],
Ignacio Larrosa Cañestro <ilarrosa at mundo-r.com> escribió:

> 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)

Sorry, it would be

 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)


>    = (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