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
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