OFFSET
1,3
COMMENTS
Originally checked to 2^65520 (or about 3*10^19723) on Nov 07 2008. - Daniel Mondot, Jan 17 2016
Conjectured to be complete. a(4), if it exists, is greater than 10^15. - Charles R Greathouse IV, Apr 06 2012
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
LINKS
Stuart A. Burrell and Han Yu, Digit expansions of numbers in different bases, arXiv:1905.00832 [math.NT], 2019.
Daniel Glasscock, Joel Moreira, and Florian K. Richter, Additive transversality of fractal sets in the reals and the integers, arXiv:2007.05480 [math.NT], 2020. See p. 5.
James Grime and Brady Haran, Why 82,000 is an extraordinary number, Numberphile video (2015)
Alex P. Klinkhamer, Digits of 82000, search algorithm with code and analysis.
EXAMPLE
82000 = 10100000001010000 (2) = 11011111001 (3) = 110001100 (4) = 10111000 (5).
MATHEMATICA
f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 2] & /@ Range[3, 5]]; Select[Range[0, 100000], f@ # == 0 &] (* Michael De Vlieger, Aug 29 2015 *)
PROG
(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
CROSSREFS
KEYWORD
bref,nonn,base
AUTHOR
Daniel Mondot, Oct 26 2008
EXTENSIONS
Edited by Charles R Greathouse IV, Nov 01 2009
Search limit extended to astronomical odds by James G. Merickel, Dec 03 2013
Search limit increased again with example code by Alex P. Klinkhamer, Aug 29 2015
Removed keywords "fini" and "full", since it is only a conjecture that there are no further terms. - N. J. A. Sloane, Feb 06 2016
STATUS
approved