OFFSET
1,1
COMMENTS
The three squares need not be distinct.
At least one of the squares must be divisible by 9.
The first term that is a concatenation of three squares in two different ways is 14411, the concatenation of 1 = 1^2, 441 = 21^2 and 1 = 1^2 and also 144 = 12^2, 1 = 1^2 and 1 = 1^2.
The first term that is a concatenation of three squares in three different ways is 1961441, the concatenation of 196 = 14^2, 144 = 12^2 and 1 = 1^2, of 196, 1 and 441 = 21^2, and of 1, 961 = 31^2 and 441.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(16) = 1049 is a term because it is the concatenation of 1 = 1^2, 0 = 0^2 and 49 = 7^2.
MAPLE
M:= 5: # for terms < 10^M
S:= {}:
for a from 1 while a^2 < 10^(M-2) do
x:= a^2; mx:= length(x);
for b from 0 while b^2 < 10^(M-1-mx) do
y:= b^2; my:= max(1, length(y));
for c from 0 while c^2 < 10^(M-mx-my) do
v:= parse(cat(x, y, c^2));
if isprime(v) then S:= S union {v} fi;
od od od:
sort(convert(S, list));
MATHEMATICA
a[maxSquareIndex_Integer?Positive]:=Select[Flatten[Table[ToExpression[IntegerString
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert Israel, Sep 29 2023
STATUS
approved