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

1, 3, 11, 111, 139

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..5.

David A. Corneth, PARI program

Jonathan Wellons, Tables of Shared Digits [archived]

Example

139^2 = 19321.

Mathematica

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 *)

Prog

(PARI) See Corneth link \\ David A. Corneth, Oct 21 2019

Crossrefs

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

Sequence in context: A105413 A241587 A183381 * A131546 A275338 A068693

Adjacent sequences: A136982 A136983 A136984 * A136986 A136987 A136988

Keyword

base,nonn,more

Author

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

Status

approved