A136863 Numbers k such that k and k^2 use only the digits 0, 1, 4 and 7.

0, 1, 10, 100, 1000, 1071, 10000, 10710, 100000, 107100, 1000000, 1071000, 10000000, 10710000, 100000000, 107100000, 1000000000, 1071000000, 10000000000, 10710000000, 100000000000, 107100000000, 1000000000000, 1071000000000, 10000000000000, 10710000000000, 100000000000000, 107100000000000

Offset

1,3

Comments

Generated with DrScheme.

Links

Table of n, a(n) for n=1..28.

Jonathan Wellons, Tables of Shared Digits [archived]

Formula

From Robert Israel, Jun 05 2025: (Start)

Conjecture: the only terms not ending in 0 are 1 and 1071. Thus for n >= 5, a(n) = 10^((n+1)/2) if n is odd, 1071 * 10^((n-6)/2) if n is even.

I have verified that any other terms not ending in 0 are greater than 10^30.

(End)

Example

107100000000000^2 = 11470410000000000000000000000.

Mathematica

With[{c={0, 1, 4, 7}}, Select[Flatten[FromDigits/@Tuples[c, 15]], SubsetQ[ c, IntegerDigits[ #^2]]&]] (* Harvey P. Dale, Feb 08 2023 *)

Crossrefs

Sequence in context: A115798 A077439 A136839 * A379980 A031201 A228989

Adjacent sequences: A136860 A136861 A136862 * A136864 A136865 A136866

Keyword

base,nonn

Author

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

Status

approved