OFFSET
1,1
COMMENTS
The sequence is infinite because all the numbers 1025*100^k are members.
It would be nice to have the subsequence of "primitive" terms, those that do not end in an even number of zeros.
Let v be a number such that v^2 starts with 1. Let w^2 have the same digits as v^2 except that the initial digit is a 2. Then (w + v) * (w - v) = w^2 - v^2 = 10^m for some integer m. For the "primitive" terms, w + v turns out to be 250, 8000, 31250 etc. w - v turns out to be 40, 1250, 3200 etc. Given such w + v and w - v it is easy to find primitive elements. Furthermore, v must lie in (sqrt(11), sqrt(20)) * sqrt(10)^i and w must lie in (sqrt(21), sqrt(30)) * sqrt(10)^i for some integer i. - David A. Corneth, May 20 2016
LINKS
Nathan Fox, Table of n, a(n) for n = 1..728
Chai Wah Wu, Primitive terms < 10^1000
EXAMPLE
1025 is a member because 11025 = 105^2 and 21025 = 145^2.
MAPLE
t1:=[];
for k from 1 to 2000000 do
if issqr(k+10^length(k)) and
issqr(k+2*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;
PROG
(PARI) is(n)=issquare(eval(Str(1, n))) && issquare(eval(Str(2, n))) \\ Charles R Greathouse IV, May 20 2016
(Magma) [n: n in [1..10000000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(1))) and IsSquare(Seqint(Intseq(n) cat Intseq(2)))]; // Marius A. Burtea, Mar 21 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
a(5)-a(17) from Alois P. Heinz, May 20 2016
STATUS
approved