A053922 Numbers k such that k^2 contains only digits {2,4,6}.

2, 8, 68, 162, 668, 5162, 6668, 25738, 66668, 79162, 163238, 666668, 6666668, 8041408, 24993332, 66666668, 666666668, 6666666668, 8016649092, 66666666668, 666666666668, 6666666666668, 66666666666668

Offset: 1

Author

Patrick De Geest, Mar 15 2000

Keywords

• nonn
• base

Comments

Conjecture: every number composed of the numeral six repeated n times and ending in the numeral 8 is a term of this sequence. - Harvey P. Dale, Jun 16 2022

From Zhao Hui Du, Mar 11 2024: (Start)

Six repeated n times and ending with 8 can be written as (6/9)*(10^n-1)+2. The square of it can be written as (4/9)*(10^(2*n)-1)+(16/9)*(10^n-1)+4. Or

444444...44444...444

+ 1777...776

+ 4

----------------------

444444...46222...224. (End)

Links

• Zhao Hui Du, Table of n, a(n) for n = 1..47
• Author?, Source(txt)

Crossrefs

Cf. A053923.

Programs

Mathematica

Select[Range[700000],SubsetQ[{2,4,6},IntegerDigits[#^2]]&] (* The program generates the first 12 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Jun 16 2022 *)

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 04 2005

Two more terms from Jon E. Schoenfield, Sep 04 2006