

A233821


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


1



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
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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



