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A053922
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Numbers k such that k^2 contains only digits {2,4,6}.
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2
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2, 8, 68, 162, 668, 5162, 6668, 25738, 66668, 79162, 163238, 666668, 6666668, 8041408, 24993332, 66666668, 666666668, 6666666668, 8016649092, 66666666668, 666666666668, 6666666666668, 66666666666668
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OFFSET
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1,1
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COMMENTS
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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
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)
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 04 2005
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STATUS
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approved
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