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
A275600
Numbers that can be written in all bases from base 2 to base 6 using only the digits 0, 1 and 2.
Original entry on oeis.org
0, 1, 2, 6, 36, 37, 260, 1302, 1376, 1380, 1381, 1382, 1556, 1560, 1561, 1562, 16932, 562500, 562501, 562502, 562506, 562512, 562536, 562537, 562752, 562760, 23610752, 23610756, 23610757, 23610786, 23615750, 23615760, 23615761, 23615762, 23615785, 23615786, 23626310
Offset: 1
16932 is in the sequence because this number can be written in bases 2 through 6 using only the digits 0, 1 and 2: 16932(b4) = 10020210 / (b5) = 1020212 / (b6) = 210220.
-
Select[Range[10^6], Function[k, Max@ Flatten@ Map[IntegerDigits[k, #] &, Range[4, 6]] < 3]] (* or *)
Select[Range[10^5], Function[k, Total@ Flatten@ Map[Take[RotateRight@ DigitCount[k, #], -(# - 3)] &, Range[4, 6]] == 0]] (* (not as efficient) Michael De Vlieger, Aug 03 2016 *)
-
nextWithSmallDigits(n, base) = my (pow=1, rem=n, val=0, d); while (rem>0, d = rem % base; rem = rem \ base; if (d>2, val = 0; rem = rem+1, val = val + d*pow); pow = pow * base); return (val)
{ n = 0; prev = 0; while (n < 300, succ = prev; for (b=4,6, succ = nextWithSmallDigits(succ, b)); if (prev==succ, n = n+1; print(n " " prev); prev = succ+1, prev = succ)) } \\ Rémy Sigrist, Sep 08 2016
-
use ntheory ":all"; my($x,$n10)=(0,0); while ($x < 50) { my $n = fromdigits( todigitstring($n10++, 3), 6); next if vecany { $ > 2 } todigits($n, 4); next if vecany { $ > 2 } todigits($n, 5); print ++$x," $n\n"; } # Dana Jacobsen, Aug 16 2016
-
from gmpy2 import digits
A275600_list = [n for n in (int(digits(m,3),6) for m in range(10**6)) if max(digits(n,5)) <= '2' and max(digits(n,4)) <= '2'] # Chai Wah Wu, Aug 15 2016
A131646
Numbers that can be written from base 2 to base 18 using only the digits 0 to 9 (conjectured to be complete).
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 20, 1027, 1028, 1029, 14745, 9020076688681, 9439828025162228377, 9439829801208141318
Offset: 1
- B. R. Barwell, Numbers Without Letters, Journal of Recreational Mathematics, Vol. 25:3 (1993), 174-179.
-
f[n_] := Total[Total@ Drop[RotateRight[DigitCount[n, #]], 10] & /@ Range[11, 18]]; Select[Range[0, 20000], f@ # == 0 &] (* Michael De Vlieger, Aug 29 2015 *)
-
isok(n) = if (n, for (b=11, 18, if (vecmax(digits(n,b))>9, return(0)))); 1; \\ Michel Marcus, Aug 30 2015
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 *)
Showing 1-4 of 4 results.
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