A300405 Numbers whose squares are the sums of two decimal repdigits.

11, 12, 38, 211

Offset

1,1

Links

Table of n, a(n) for n=1..4.

Bart Goddard, Jeremy Rouse, Sum of two repdigits a square, Integers 17 (2017), #A24, Theorem 1.

Example

11^2 = 99 + 22 = 88 + 33 = 77 + 44 = 66 + 55,
12^2 = 111 + 33,
38^2 = 1111 + 333,
211^2 = 44444 + 77.

Mathematica

With[{s = Transpose@ Table[FromDigits@ ConstantArray[i, j], {i, 9}, {j, 2, 20}]}, Sqrt@ Union@ Select[Map[Total, Subsets[Flatten@ s, {2}]], IntegerQ@ Sqrt@ # &]]

Crossrefs

Cf. A010785.

Sequence in context: A041250 A225299 A290336 * A248323 A291059 A041254

Adjacent sequences: A300402 A300403 A300404 * A300406 A300407 A300408

Keyword

nonn,base,fini,full

Author

Michael De Vlieger, Apr 03 2018

Status

approved