A146025
Numbers that can be written in bases 2, 3, 4, and 5 using only the digits 0 and 1.
Original entry on oeis.org
82000 = 10100000001010000 (2) = 11011111001 (3) = 110001100 (4) = 10111000 (5).
- 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.
-
f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 2] & /@ Range[3, 5]]; Select[Range[0, 100000], f@ # == 0 &] (* Michael De Vlieger, Aug 29 2015 *)
-
is(n)=vecmax(digits(n,5))<2 && vecmax(digits(n,4))<2 && vecmax(digits(n,3))<2 \\ Charles R Greathouse IV, Aug 31 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
A146026
Numbers that can be written from base 2 to base 9 using only the digits 0 to 3.
Original entry on oeis.org
0, 1, 2, 3, 8281, 8282, 8283
Offset: 1
-
Select[Range[0, 10^5], Function[n, Times @@ Boole@ Map[Max@ IntegerDigits[n, #] <= 3 &, Range[2, 9]] > 0]] (* Michael De Vlieger, Aug 15 2016 *)
A146027
Numbers that can be written from base 2 to base 10 using only the digits 0 to 4.
Original entry on oeis.org
0, 1, 2, 3, 4, 10, 100, 140004, 140304, 140312, 1131032, 1131033, 1131034, 1131040
Offset: 1
-
imax:= 20: # to consider numbers < 6^imax
L:= Matrix(5,imax):
Delta:= proc(L,b)
local i,j,m,Lloc;
if max(L) <= 4 then return 0 fi;
Lloc:= L;
m:= 0;
for j from 1 to imax while max(Lloc[j..imax]) > 4 do
m:= m + b^(j-1)*(b-Lloc[j]);
if j < imax then Lloc[j+1]:= Lloc[j+1]+1 fi
od;
m
end proc:
n:= 0: count:= 1: A[1]:= 0:
isdone:= false;
while max(L[..,imax]) < 5 and not isdone do
n:= n+1;
L[..,1]:= L[..,1]+<1,1,1,1,1>;
m:= max(seq(Delta(L[b-5,..],b),b=6..10));
while m > 0 and not isdone do
n:= n+m;
for b from 6 to 10 do
Lb:= convert(n,base,b);
if nops(Lb) > imax then isdone:= true; break fi;
L[b-5,1..nops(Lb)]:= Vector[row](Lb);
od:
m:= max(seq(Delta(L[b-5,..],b),b=6..10));
od;
if not isdone then
count:= count+1;
A[count]:= n;
fi
od:
seq(A[i],i=1..count); # Robert Israel, Aug 31 2015
-
f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 5] & /@ Range[6, 10]]; Select[Range[0, 1200000], f@ # == 0 &] (* Aug 29 2015, or *)
Select[Range[0, 1200000], Function[n, Times @@ Boole@ Map[Max@ IntegerDigits[n, #] <= 4 &, Range[2, 10]] > 0]] (* Michael De Vlieger, Aug 15 2016 *)
-
isok(n) = if (n, for (b=6, 10, if (vecmax(digits(n,b))>4, return(0)))); 1; \\ Michel Marcus, Aug 30 2015
A146028
Numbers that can be written from base 2 to base 15 using only the digits 0 to 7.
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 15, 16, 174731235562130, 174731235562131, 174731235562132, 174731235562143, 174731235562147, 174731235562170, 174731235562171, 174731235564710, 174731235564711, 174731236371006, 25354527232277132536350, 25354527232277132536351
Offset: 1
-
Select[Range[0, 10^5], Function[n, Times @@ Boole@ Map[Max@ IntegerDigits[n, #] <= 7 &, Range[2, 15]] > 0]] (* Michael De Vlieger, Aug 15 2016 *)
A146029
Numbers that can be written from base 2 to base 17 using only the digits 0 to 8 (conjectured to be complete).
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 8, 17, 18
Offset: 1
-
Select[Range[0, 10^5], Function[n, Times @@ Boole@ Map[Max@ IntegerDigits[n, #] <= 8 &, Range[2, 17]] > 0]] (* Michael De Vlieger, Aug 15 2016 *)
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