

A230604


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


1



11, 173, 264, 16262, 193744, 238165, 38981039, 112791955, 1580178016, 1052631579, 30762132977, 15020242915, 14451789007487
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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% (onesigma).  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[lnn+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



