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 A136859 Numbers k such that k and k^2 use only the digits 0, 1, 4 and 6. 3
 0, 1, 4, 10, 40, 100, 400, 1000, 4000, 10000, 40000, 100000, 400000, 1000000, 4000000, 10000000, 40000000, 100000000, 400000000, 1000000000, 4000000000, 10000000000, 40000000000, 100000000000, 400000000000, 1000000000000, 4000000000000, 10000000000000, 40000000000000, 100000000000000, 400000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Generated with DrScheme. Are the formulas conjectured or proved? For example, the analogous sequence for {0,1,2,4} contains the sporadic solution 1010000104010000101. Clearly, if a(n) is in the sequence then 10*a(n) is also in the sequence. Is there any term that is not 0, 1, or 4 times a power of 10? - M. F. Hasler, Jan 26 2016 Answer: the formulas were merely conjectures. It appears that it is an open question as to whether there is any other type of term. - N. J. A. Sloane, Jan 29 2016 David W. Wilson has observed that the real number n = 2/3 = 0.66666... with n^2 = 4/9 = 0.44444... (almost) satisfies the requirement of this sequence. - N. J. A. Sloane, Jan 30 2016 LINKS David W. Wilson, Table of n, a(n) for n = 1..61 Jonathan Wellons, Tables of Shared Digits [archived]. FORMULA Conjectures from Philippe Deléham, Mar 11 2014: (Start) G.f.: x^2*(1+4*x)/(1-10*x^2); a(1) = 0, a(2) = 1, a(3) = 4, a(n) = 10*a(n-2) for n>3. (End) This yields: a(n) = 4^(n mod 2)*A178501(floor(n/2)), where A178501(n) = floor(10^(k-1)). - M. F. Hasler, Nov 09 2017 EXAMPLE 400000000000000^2 = 160000000000000000000000000000. MATHEMATICA clearQ[n_]:=Module[{dc = DigitCount[n]}, dc[[2]] == dc[[3]] == dc[[5]] == dc[[7]] == dc[[8]] == dc[[9]] == 0] Select[Range[0, 2*10^6], clearQ[#]&&clearQ[#^2] &] (* Vincenzo Librandi, Feb 02 2016 *) CROSSREFS Cf. A000290, A178501. Sequence in context: A077811 A136855 A136860 * A051479 A149204 A149205 Adjacent sequences: A136856 A136857 A136858 * A136860 A136861 A136862 KEYWORD base,nonn AUTHOR Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008 EXTENSIONS Replaced formulas by conjectures, deleted b-file and computer program based on these conjectures. - N. J. A. Sloane, Jan 29 2016 M. F. Hasler, Jan 29 2016, reports that he has confirmed that the terms shown are complete up to a(31) = 400000000000000. - N. J. A. Sloane, Jan 30 2016 Extended b-file with complete values up to a(61). - David W. Wilson, Feb 01 2016 STATUS approved

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Last modified August 10 16:44 EDT 2024. Contains 375058 sequences. (Running on oeis4.)