cp's OEIS Frontend

A146027 Numbers that can be written from base 2 to base 10 using only the digits 0 to 4.

%I A146027 #44 May 03 2019 08:40:21
%S A146027 0,1,2,3,4,10,100,140004,140304,140312,1131032,1131033,1131034,1131040
%N A146027 Numbers that can be written from base 2 to base 10 using only the digits 0 to 4.
%C A146027 Conjectured to be complete.
%C A146027 Checked on Oct 31 2008 up to 2^16384 (or 1.2*10^4932). - _Daniel Mondot_, Jan 17 2016
%C A146027 No more entries < 10^78. - _Robert Israel_, Aug 31 2015
%C A146027 It is a plausible conjecture that there are no more terms, but this has not been proved. - _N. J. A. Sloane_, Nov 17 2017
%H A146027 Stuart A. Burrell, Han Yu, <a href="https://arxiv.org/abs/1905.00832">Digit expansions of numbers in different bases</a>, arXiv:1905.00832 [math.NT], 2019.
%p A146027 imax:= 20: # to consider numbers < 6^imax
%p A146027 L:= Matrix(5,imax):
%p A146027 Delta:= proc(L,b)
%p A146027   local i,j,m,Lloc;
%p A146027   if max(L) <= 4 then return 0 fi;
%p A146027   Lloc:= L;
%p A146027   m:= 0;
%p A146027   for j from 1 to imax while max(Lloc[j..imax]) > 4 do
%p A146027           m:= m + b^(j-1)*(b-Lloc[j]);
%p A146027           if j < imax then Lloc[j+1]:= Lloc[j+1]+1 fi
%p A146027   od;
%p A146027   m
%p A146027 end proc:
%p A146027 n:= 0: count:= 1: A[1]:= 0:
%p A146027 isdone:= false;
%p A146027 while max(L[..,imax]) < 5 and not isdone do
%p A146027   n:= n+1;
%p A146027   L[..,1]:= L[..,1]+<1,1,1,1,1>;
%p A146027   m:= max(seq(Delta(L[b-5,..],b),b=6..10));
%p A146027   while m > 0 and not isdone do
%p A146027     n:= n+m;
%p A146027     for b from 6 to 10 do
%p A146027        Lb:= convert(n,base,b);
%p A146027        if nops(Lb) > imax then isdone:= true; break fi;
%p A146027        L[b-5,1..nops(Lb)]:= Vector[row](Lb);
%p A146027     od:
%p A146027     m:= max(seq(Delta(L[b-5,..],b),b=6..10));
%p A146027   od;
%p A146027   if not isdone then
%p A146027     count:= count+1;
%p A146027     A[count]:= n;
%p A146027   fi
%p A146027 od:
%p A146027 seq(A[i],i=1..count); # _Robert Israel_, Aug 31 2015
%t A146027 f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 5] & /@ Range[6, 10]]; Select[Range[0, 1200000], f@ # == 0 &] (* Aug 29 2015, or *)
%t A146027 Select[Range[0, 1200000], Function[n, Times @@ Boole@ Map[Max@ IntegerDigits[n, #] <= 4 &, Range[2, 10]] > 0]] (* _Michael De Vlieger_, Aug 15 2016 *)
%o A146027 (PARI) isok(n) = if (n, for (b=6, 10, if (vecmax(digits(n,b))>4, return(0)))); 1; \\ _Michel Marcus_, Aug 30 2015
%Y A146027 Cf. A146025, A146026, A146028, A131646, A275600.
%K A146027 nonn,base
%O A146027 1,3
%A A146027 _Daniel Mondot_, Oct 26 2008
%E A146027 Edited by _Charles R Greathouse IV_, Nov 01 2009