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A146025
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Numbers that can be written in bases 2, 3, 4, and 5 using only the digits 0 and 1.
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12
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OFFSET
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1,3
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COMMENTS
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Originally checked to 2^65520 (or about 3*10^19723) on Nov 07 2008. - Daniel Mondot, Jan 17 2016
Checked to 3125 (5^5) base-5 digits in just under 1/2 hour using a minor modification of the PARI program at A230360. Interestingly, with 5 replaced by 9 and the digits 2 and 3 permitted, it appears the complete set is--somewhat coincidental with this--{0, 1, 2, 3, 8281, 8282, 8283}, see A146026. - James G. Merickel, Dec 01 2013
Checked to 11 million decimal digits in 1 week using an algorithm that, upon finding that the current guess has non-{0,1} digits in a particular base, increases the guess to only have {0,1} digits in that base. C code in links. - Alex P. Klinkhamer, Aug 29 2015
It is a plausible conjecture that there are no more terms, but this has not been proved. - N. J. A. Sloane, Feb 06 2016
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LINKS
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Alex P. Klinkhamer, Digits of 82000, search algorithm with code and analysis.
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EXAMPLE
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82000 = 10100000001010000 (2) = 11011111001 (3) = 110001100 (4) = 10111000 (5).
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MATHEMATICA
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f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 2] & /@ Range[3, 5]]; Select[Range[0, 100000], f@ # == 0 &] (* Michael De Vlieger, Aug 29 2015 *)
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PROG
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(PARI) is(n)=vecmax(digits(n, 5))<2 && vecmax(digits(n, 4))<2 && vecmax(digits(n, 3))<2 \\ Charles R Greathouse IV, Aug 31 2015
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CROSSREFS
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KEYWORD
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bref,nonn,base
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AUTHOR
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EXTENSIONS
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Removed keywords "fini" and "full", since it is only a conjecture that there are no further terms. - N. J. A. Sloane, Feb 06 2016
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STATUS
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approved
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