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A131646 Numbers that can be written from base 2 to base 18 using only the digits 0 to 9 (conjectured to be complete). 5

%I #25 Nov 19 2017 13:24:30

%S 0,1,2,3,4,5,6,7,8,9,18,19,20,1027,1028,1029,14745,9020076688681,

%T 9439828025162228377,9439829801208141318

%N Numbers that can be written from base 2 to base 18 using only the digits 0 to 9 (conjectured to be complete).

%C Originally checked to 2^20356 (or 5.8*10^6127) in Nov 2008.

%C It appears that 19 and 20 are the only numbers > 9 that can be written up to base 19 only using digits 0 to 9 and 20 is the only number > 9 that can be written up to base 20 only using digits 0 to 9.

%C It is a plausible conjecture that there are no more terms, but this has not been proved. - _N. J. A. Sloane_, Nov 17 2017

%D B. R. Barwell, Numbers Without Letters, Journal of Recreational Mathematics, Vol. 25:3 (1993), 174-179.

%H Daniel Mondot, <a href="http://archives.forumenigmes.net/index.php?showtopic=6347">Related Puzzle</a>.

%t f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 10] & /@ Range[11, 18]]; Select[Range[0, 20000], f@ # == 0 &] (* _Michael De Vlieger_, Aug 29 2015 *)

%o (PARI) isok(n) = if (n, for (b=11, 18, if (vecmax(digits(n,b))>9, return(0)))); 1; \\ _Michel Marcus_, Aug 30 2015

%Y Cf. A146025, A146026, A146027, A146028, A146029.

%K nonn,base

%O 1,3

%A _Daniel Mondot_, Sep 08 2007, Nov 02 2008

%E Edited by _Charles R Greathouse IV_, Nov 01 2009

%E Reference added by _William Rex Marshall_, Oct 23 2011

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)