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%I #32 Mar 11 2024 05:53:00
%S 2,8,68,162,668,5162,6668,25738,66668,79162,163238,666668,6666668,
%T 8041408,24993332,66666668,666666668,6666666668,8016649092,
%U 66666666668,666666666668,6666666666668,66666666666668
%N Numbers k such that k^2 contains only digits {2,4,6}.
%C 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
%C From _Zhao Hui Du_, Mar 11 2024: (Start)
%C 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
%C 444444...44444...444
%C + 1777...776
%C + 4
%C ----------------------
%C 444444...46222...224. (End)
%H Zhao Hui Du, <a href="/A053922/b053922.txt">Table of n, a(n) for n = 1..47</a>
%H Author?, <a href="http://web.archive.org/web/20080708203024/http://blue.kakiko.com/mmrmmr/htm/eqtn06.html">Source</a>(<a href="http://web.archive.org/web/20060426155831/http://blue.kakiko.com/mmrmmr/txt/eqtn06.txt">txt</a>)
%t 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 *)
%Y Cf. A053923.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Mar 15 2000
%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 04 2005
%E Two more terms from _Jon E. Schoenfield_, Sep 04 2006
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