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URL: https://oeis.org/A053922

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A053922
Numbers k such that k^2 contains only digits {2,4,6}.
2
2, 8, 68, 162, 668, 5162, 6668, 25738, 66668, 79162, 163238, 666668, 6666668, 8041408, 24993332, 66666668, 666666668, 6666666668, 8016649092, 66666666668, 666666666668, 6666666666668, 66666666666668
OFFSET
1,1
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
Author?, Source(txt)
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 *)
CROSSREFS
Cf. A053923.
Sequence in context: A226730 A202553 A023164 * A385051 A030445 A093990
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Mar 15 2000
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
STATUS
approved