A233821 Smallest zeroless number x such that x^n has exactly n zero digits.

245, 126, 245, 321, 351, 1244, 194, 4648, 951, 4357, 3757, 2169, 2392, 7399, 8379, 9723, 8683, 13867, 6152, 24887, 18898, 55825, 54631, 29647, 35586, 46564, 67743, 84789, 119421, 72296, 43642, 92233, 44411, 142553, 126693, 135852, 52299, 229626, 143951

Offset

2,1

Links

Table of n, a(n) for n=2..40.

Example

951 has no zeros and 951^10 has ten zeros (605069371210073000039238122001). This is the least positive integer with this property.

Maple

N:= 30: # to get terms up to a(N)
for n from 2 to N do
  for k from 1 do
     if numboccur(0, convert(k, base, 10)) = 0 and
        numboccur(0, convert(k^n, base, 10)) = n then
          A[n]:= k;
          break
     fi
  od
od:
seq(A[n], n=2..N); # Robert Israel, Aug 05 2014

Prog

(Python)
def GetNums(x):
..for n in range(10**6):
....if str(n).count("0") == 0:
......if str(n**x).count("0") == x:
........return n
x = 2
while x < 50:
..print(GetNums(x), end=', ')
..x += 1
(PARI) okxn(x, n) = {ok = 0; if (vecmin (digits(x)), dxn = digits(x^n); ok = (sum(i=1, #dxn, dxn[i] == 0) == n); ); ok; }
a(n) = {x=1; while (! okxn(x, n), x++); x; } \\ Michel Marcus, Dec 23 2013

Crossrefs

Cf. A052382.

Sequence in context: A291587 A220090 A013684 * A216233 A157246 A186460

Adjacent sequences: A233818 A233819 A233820 * A233822 A233823 A233824

Keyword

nonn,base

Author

Derek Orr, Dec 16 2013

Extensions

More terms from Michel Marcus, Dec 23 2013

Definition edited by Robert Israel, Aug 05 2014

Definition simplified by Derek Orr, Mar 23 2015

Status

approved