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 A146025 Numbers that can be written in bases 2, 3, 4, and 5 using only the digits 0 and 1. 12
 0, 1, 82000 (list; graph; refs; listen; history; text; internal format)
 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 Intersection of A005836, A000695, and A033042. Cf. A258981 (bases 2,3,4), A258107 (bases 2..n). Cf. A131646, A146026, A146027, A230360, A275600. Sequence in context: A134122 A138044 A098187 * A283418 A330872 A253957 Adjacent sequences:  A146022 A146023 A146024 * A146026 A146027 A146028 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

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Last modified January 21 00:46 EST 2022. Contains 350473 sequences. (Running on oeis4.)