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

1,1

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

Links

Table of n, a(n) for n=1..21.

Example

4000171725^2 = 16001373829489475625.

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 *)

Crossrefs

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

Sequence in context: A092380 A096566 A217051 * A199630 A198298 A074773

Adjacent sequences: A198860 A198861 A198862 * A198864 A198865 A198866

Keyword

nonn,base,fini

Author

Pablo Martínez, Oct 30 2011

Extensions

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

Status

approved