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A136808
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Numbers k such that k and k^2 use only the digits 0, 1 and 2.
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13
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0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1011, 1100, 1101, 10000, 10001, 10010, 10011, 10100, 10110, 11000, 11001, 11010, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101100, 110000, 110001, 110010, 110100, 1000000, 1000001, 1000010, 1000011, 1000100
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OFFSET
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1,3
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COMMENTS
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Generated with DrScheme.
A278038(18) = 10101, A136827(294) = 10110001101, A136831(1276) = 101100010001101 resp. A136836(1262) = 101090009991101 are the first terms from where on these four sequences differ from the present one. - M. F. Hasler, Nov 15 2017
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LINKS
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EXAMPLE
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101000100100001^2 = 10201020220210222010200200001.
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MAPLE
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isA136808 := proc(n) local ndgs, n2dgs ; ndgs := convert(convert(n, base, 10), set) ; n2dgs := convert(convert(n^2, base, 10), set) ; if ( (ndgs union n2dgs) minus {0, 1, 2} ) = {} then true ; else false ; fi ; end: LtonRev := proc(L) local i ; add(op(i, L)*10^(i-1), i=1..nops(L)) ; end: A007089 := proc(n) convert(n, base, 3) ; LtonRev(%) ; end: n := 1: for i from 0 do n3 := A007089(i) ; if isA136808(n3) then printf("%d %d ", n, n3) ; n := n+1 ; fi ; od: # R. J. Mathar, Jan 24 2008
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MATHEMATICA
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Select[FromDigits/@Tuples[{0, 1}, 7], Union[Take[DigitCount[#^2], {3, 9}]]=={0}&] (* Harvey P. Dale, May 29 2013 *)
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PROG
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(PARI) for(n=1, 999, vecmax(digits((N=fromdigits(binary(n), 10))^2))<3 && print1(N", ")) \\ M. F. Hasler, Nov 15 2017
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CROSSREFS
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Subsequence of A278038 (binary numbers without '111'), in turn a subsequence of the binary numbers A007088.
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KEYWORD
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nonn,base
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AUTHOR
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Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008
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STATUS
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approved
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