OFFSET
1,2
COMMENTS
For any x > 0, if d is large enough there are squares between 10^d*x + 10^(d-1) and 10^d*x + 10^d - 1. Thus the sequence is infinite.
a(3) = 4 is the minimum value of a(n) for n > 1. - Altug Alkan, Nov 24 2015 (This is because no square can end in 2 or 3, so 2 and 3 can never appear in the sequence. - N. J. A. Sloane, Nov 24 2015)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
For n = 6, a(n-1) = 61. There are no squares of the form 61x or 61xy with x>=1. The least square of the form 61xyz with x >= 1 is 61504, and 504 has not appeared previously so a(6) = 504.
MAPLE
S:= {1};
A[1]:= 1;
for n from 2 to 100 do
found:= false;
x:= A[n-1];
for d from 1 while not found do
a:= ceil(sqrt(10^d*x +10^(d-1)));
b:= floor(sqrt(10^d*x + 10^d - 1));
Q:= map(t -> t^2 - 10^d*x, {$a..b}) minus S;
if nops(Q) >= 1 then
A[n]:= min(Q);
S:= S union {A[n]};
found:= true;
fi
od
od:
seq(A[n], n=1..100);
MATHEMATICA
(*to get B numbers of the sequence*) A={1}; i=1; While[i<B, i++; m=Last[A]; d=0; flag=0; While[flag==0, d++; g0=Ceiling[Sqrt[m*10^d+10^(d-1)]]; h=(m+1)10^d; a=g0; Label[L$]; If[a^2<h, b=a^2-m*10^d; If[MemberQ[A, b], a++; Goto[L$], flag=1; AppendTo[A, b]]]]]; A (* Emmanuel Vantieghem, Nov 24 2015 *)
PROG
(PARI) A264770(n, show=0, a=1, u=[])={for(n=2, n, u=setunion(u, [a]); show&&print1(a", "); my(k=3); until(!setsearch(u, k++) && issquare(eval(Str(a, k))), ); a=k); a} \\ Use optional 2nd, 3rd or 4th argument to print intermediate terms, use another starting value, or exclude some numbers. - M. F. Hasler, Nov 24 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert Israel, Nov 24 2015, following a suggestion from N. J. A. Sloane.
STATUS
approved