A096913 Numbers n such that (largest digit of n)^(smallest digit of n) + n is a square.

0, 13, 72, 80, 91, 120, 137, 163, 188, 251, 275, 281, 317, 321, 360, 388, 391, 440, 495, 527, 627, 840, 891, 960, 1023, 1088, 1148, 1151, 1288, 1363, 1437, 1520, 1591, 1674, 1680, 1757, 1841, 1927, 2024, 2113, 2208, 2303, 2365, 2400, 2464, 2491, 2565, 2600

Offset

1,2

Comments

Conjecture: 0 and 3844 are the only squares in this sequence.

There are only finitely many squares in the sequence because for some square big enough the offset to the next square is greater than 9^9. Now, for each number d = (largest digit of n)^(smallest digit of n) we just have to walk through the squares, check if this square has the correct (largest digit of n)^(smallest digit of n) property and added d is also a square. I have done that search computation exhaustively (using a PARI program). There are no more squares. - Maon Wenders, Jun 02 2012

This sequence has infinitely many terms because there are infinitely many numbers b^2 - 1 that contain a zero in their decimal expansion. - T. D. Noe, Jul 20 2012

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

388 is in the sequence because 8^3 + 388 = 900 = 30^2.

Mathematica

Join[{0}, Select[Range[3000], IntegerQ[Sqrt[Max[IntegerDigits[#]]^ Min[ IntegerDigits[ #]]+ #]]&]] (* Harvey P. Dale, Sep 14 2018 *)

Crossrefs

Cf. A054054, A054055.

Sequence in context: A141989 A159512 A104132 * A026916 A106173 A094943

Adjacent sequences: A096910 A096911 A096912 * A096914 A096915 A096916

Keyword

base,easy,nonn

Author

Jason Earls, Aug 17 2004

Status

approved