A230604 - OEIS

%I #67 Oct 14 2024 17:55:38

%S 11,173,264,16262,193744,238165,38981039,112791955,1580178016,

%T 1052631579,30762132977,15020242915,14451789007487,10909090909091,

%U 1242844268897055,1001889106154509,4024018444782046,10018891061545090,11678332116788271168,102040816316530612245,139009056141395353279,1128182832632197435939

%N Smallest number whose square has more than n digits and begins and ends with the same n digits.

%C Differs from A161355 in that the present sequence allows an "overlap" of the digits, while A161355 requires a(n)^2 to have at least 2n digits. - _M. F. Hasler_, Mar 03 2014

%H Max Alekseyev, <a href="/A230604/b230604.txt">Table of n, a(n) for n = 1..32</a>

%e a(3)=264 since 264^2 = 69696 is the smallest square that starts and ends with the same 3 digits.

%t a[n_] := Block[{digits = {}},

%t   For[i = Ceiling[Sqrt[10^n]], True, i++,

%t    If[i^2 >= 10^n, digits = IntegerDigits[i^2];

%t     If[Take[digits, n] == Take[digits, -n], Return[i]]]]];

%t a2[#] & /@ Range[1, 6] (* _Julien Kluge_, Feb 02 2016 *)

%o (PARI) for(n=1, 8, k=floor(sqrt(10^n)); until(bn==ed, k++; sr=Str(k^2); vc=Vec(sr); ln=#sr; bn=vc[1..n]; ed=vc[ln-n+1..ln]); print1(k, ", "));

%Y Cf. A116501, A161355.

%K nonn,base

%O 1,1

%A _Arkadiusz Wesolowski_, Feb 28 2014

%E a(9)-a(10) from _Julien Kluge_, Feb 13 2016

%E a(11)-a(12) from _Julien Kluge_, Mar 04 2016

%E a(13) from _Giovanni Resta_, Apr 18 2016

%E Terms a(14) onward from _Max Alekseyev_, Oct 11 2024