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A146027 Numbers that can be written from base 2 to base 10 using only the digits 0 to 4. 6
0, 1, 2, 3, 4, 10, 100, 140004, 140304, 140312, 1131032, 1131033, 1131034, 1131040 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..14.

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

Cf. A146025, A146026, A146028, A131646, A275600.

Sequence in context: A045924 A244551 A068910 * A305619 A035358 A265351

Adjacent sequences:  A146024 A146025 A146026 * A146028 A146029 A146030

KEYWORD

nonn,base

AUTHOR

Daniel Mondot, Oct 26 2008

EXTENSIONS

Edited by Charles R Greathouse IV, Nov 01 2009

STATUS

approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)