A137144 -id:A137144 - cp's OEIS frontend

A136985 Numbers k such that k and k^2 use only the digits 1, 2, 3 and 9.

1, 3, 11, 111, 139

Offset: 1

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Generated with DrScheme.
No additional terms < 10^11. - Harvey P. Dale, Oct 21 2019
From David A. Corneth, Oct 21 2019: (Start)
No additional terms < 10^31.
The final digits of 1^2, 2^2, 3^2 and 9^2 are 1, 4, 9 and 1 respectively, of which only 1 and 9 are allowed. So a term must end in 1, 3 or 9.
Checking two digits, we see that only numbers ending in 11, 23, 39 or 99 squared have the last two digits allowed.
Similar for three digits, a term must end in one of 111, 911, 123, 323, 923, 139, 239, 339 or 999.
We can recursively see how a number must end and hence reduce the numbers that must be checked. For example, we only have to check 4204352 31-digit numbers to know there are no 31-digit terms.
(End)
No additional terms < 10^38. - Michael S. Branicky, Jul 05 2021

			139^2 = 19321.

David A. Corneth, PARI program
Jonathan Wellons, Tables of Shared Digits [archived]

Cf. A077439, A136809, A136813, A137028, A137105, A137144, A137147.

With[{c={1,2,3,9}},Select[Flatten[Table[FromDigits/@Tuples[c,n],{n,3}]],SubsetQ[ c,IntegerDigits[#^2]]&]] (* Harvey P. Dale, Oct 21 2019 *)

\\ See Corneth link. David A. Corneth, Oct 21 2019

cp's OEIS Frontend

A136985 Numbers k such that k and k^2 use only the digits 1, 2, 3 and 9.

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