A198863 Numbers whose squares are pandigital numbers with exactly two occurrences of each digit.

3164252736, 3164326683, 3164389113, 3164391957, 3164406057, 3164416923, 3164421333, 3164454864, 3164466768, 3164482974, 3164528124, 3164547114, 3164689392, 3164695206, 3164735277, 3164770866, 3164789766, 3164863185, 3164867118, 3164907357, 3165009693

Offset: 1

Author

Pablo Martínez, Oct 30 2011

Keywords

• nonn
• base
• fini

Comments

Later terms include: 4000171725, 4000183233, 4000198443, 4000203567.

Because the sum of the digits of a(n)^2 is 90, 9 divides a(n)^2. Hence, 3 divides a(n). - T. D. Noe, Nov 08 2011

Examples

			4000171725^2 = 16001373829489475625.
		

Crossrefs

Cf. A156977 (n^2 contains each digit once).

Programs

Mathematica

Select[Range[3164250000, 3164450000], Union[DigitCount[#^2]] == {2} &] (* Alonso del Arte, Oct 31 2011 *)
t = {}; n = 3164211348; nMax = 9994386752; While[n <= nMax && Length[t] < 21, While[n <= nMax && Union[DigitCount[n^2]] != {2}, n = n + 3]; If[n <= nMax, AppendTo[t, n]; Print[n]; n = n + 3]]; t (* T. D. Noe, Nov 08 2011 *)

Extensions

All displayed terms are from Charles R Greathouse IV, Alonso del Arte and T. D. Noe, Nov 08 2011