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A052040
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Numbers whose square is zeroless.
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19
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1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 54, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 96
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OFFSET
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1,2
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COMMENTS
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This sequence is infinite, since 33...334^2 = 11...11155...556, for example. This answers an open problem stated in HAKMEM. - Karl W. Heuer, Aug 19 2015
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LINKS
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Michael Beeler, R. William Gosper, and Rich Schroeppel, "HAKMEM" Item 36, Memo 239, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Mass., 1972.
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EXAMPLE
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31 is a term: 31^2 = 961 has no 0's among its digits.
32 is not a term, because 32^2 = 1024. (End)
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MATHEMATICA
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Select[Range[0, 100], DigitCount[#^2, 10, 0]==0 &] (* Vincenzo Librandi, Feb 22 2015 *)
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PROG
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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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STATUS
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approved
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