OFFSET
1,3
COMMENTS
Conjectured to be complete.
Checked on Oct 31 2008 up to 2^16384 (or 1.2*10^4932). - Daniel Mondot, Jan 17 2016
No more entries < 10^78. - Robert Israel, Aug 31 2015
It is a plausible conjecture that there are no more terms, but this has not been proved. - N. J. A. Sloane, Nov 17 2017
LINKS
Stuart A. Burrell, Han Yu, Digit expansions of numbers in different bases, arXiv:1905.00832 [math.NT], 2019.
MAPLE
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
MATHEMATICA
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 *)
PROG
(PARI) isok(n) = if (n, for (b=6, 10, if (vecmax(digits(n, b))>4, return(0)))); 1; \\ Michel Marcus, Aug 30 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Daniel Mondot, Oct 26 2008
EXTENSIONS
Edited by Charles R Greathouse IV, Nov 01 2009
STATUS
approved