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A233821 Smallest zeroless number x such that x^n has exactly n zero digits. 1

%I #28 Mar 26 2015 13:59:13

%S 245,126,245,321,351,1244,194,4648,951,4357,3757,2169,2392,7399,8379,

%T 9723,8683,13867,6152,24887,18898,55825,54631,29647,35586,46564,67743,

%U 84789,119421,72296,43642,92233,44411,142553,126693,135852,52299,229626,143951

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

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

%p N:= 30: # to get terms up to a(N)

%p for n from 2 to N do

%p for k from 1 do

%p if numboccur(0,convert(k,base,10)) = 0 and

%p numboccur(0,convert(k^n, base, 10)) = n then

%p A[n]:= k;

%p break

%p fi

%p od

%p od:

%p seq(A[n],n=2..N); # _Robert Israel_, Aug 05 2014

%o (Python)

%o def GetNums(x):

%o ..for n in range(10**6):

%o ....if str(n).count("0") == 0:

%o ......if str(n**x).count("0") == x:

%o ........return n

%o x = 2

%o while x < 50:

%o ..print(GetNums(x),end=', ')

%o ..x += 1

%o (PARI) okxn(x, n) = {ok = 0; if (vecmin (digits(x)), dxn = digits(x^n); ok = (sum(i=1, #dxn, dxn[i] == 0) == n);); ok;}

%o a(n) = {x=1; while (! okxn(x, n), x++); x;} \\ _Michel Marcus_, Dec 23 2013

%Y Cf. A052382.

%K nonn,base

%O 2,1

%A _Derek Orr_, Dec 16 2013

%E More terms from _Michel Marcus_, Dec 23 2013

%E Definition edited by _Robert Israel_, Aug 05 2014

%E Definition simplified by _Derek Orr_, Mar 23 2015

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)