

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
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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



FORMULA

G.f.: x^2*(1+4*x)/(110*x^2);
a(1) = 0, a(2) = 1, a(3) = 4, a(n) = 10*a(n2) for n>3. (End)


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



KEYWORD

base,nonn


AUTHOR

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008


EXTENSIONS

Replaced formulas by conjectures, deleted bfile 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 bfile with complete values up to a(61).  David W. Wilson, Feb 01 2016


STATUS

approved



