A230604 Smallest number whose square has more than n digits and begins and ends with the same n digits.

11, 173, 264, 16262, 193744, 238165, 38981039, 112791955, 1580178016, 1052631579, 30762132977, 15020242915, 14451789007487

Offset

1,1

Comments

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

According to a linear regression, a(13) is in the range (1.2 +/- 1.0)*10^12 with a probability of 68.3% (one-sigma). - Julien Kluge, Mar 04 2016

Links

Table of n, a(n) for n=1..13.

Example

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

Mathematica

a[n_] := Block[{digits = {}},
  For[i = Ceiling[Sqrt[10^n]], True, i++,
   If[i^2 >= 10^n, digits = IntegerDigits[i^2];
    If[Take[digits, n] == Take[digits, -n], Return[i]]]]];
a2[#] & /@ Range[1, 6] (* Julien Kluge, Feb 02 2016 *)

Prog

(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, ", "));

Crossrefs

Cf. A116501, A161355.

Sequence in context: A307168 A141955 A133243 * A161355 A223067 A280442

Adjacent sequences: A230601 A230602 A230603 * A230605 A230606 A230607

Keyword

nonn,base,more

Author

Arkadiusz Wesolowski, Feb 28 2014

Extensions

a(9)-a(10) from Julien Kluge, Feb 13 2016

a(11)-a(12) from Julien Kluge, Mar 04 2016

a(13) from Giovanni Resta, Apr 18 2016

Status

approved