cp's OEIS Frontend

A090493 Least k such that n^k contains all the digits from 0 through 9, or 0 if no such k exists.

%I A090493 #67 Aug 17 2021 02:23:51
%S A090493 0,68,39,34,19,20,18,28,24,0,23,22,22,21,12,17,14,21,17,51,17,18,14,
%T A090493 19,11,18,13,11,12,39,11,14,16,14,19,10,13,14,17,34,11,17,13,16,15,11,
%U A090493 12,12,9,18,16,11,13,10,12,7,13,11,11,20,14,18,13,14,10,13,10,9,11,18,15
%N A090493 Least k such that n^k contains all the digits from 0 through 9, or 0 if no such k exists.
%C A090493 Note that the values of n for which a(n) = 1 have density 1.
%C A090493 Is it known that a(n)=0 only for n a power of 10? - _Christopher J. Smyth_, Aug 21 2014
%C A090493 a(n) >= ceiling(log_n(10)*9), whenever a(n)>0. This is because in order for an integer to have 10 digits its base-10 magnitude must be at least 9. - _Ely Golden_, Sep 06 2017
%H A090493 Seiichi Manyama, <a href="/A090493/b090493.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A090493 Ely Golden, <a href="/A090493/a090493.py.txt">Python program to generate a(n)</a>
%F A090493 a(10^e) = 0; a(m^e) = a(m)/e for e dividing a(m). - _Reinhard Zumkeller_, Dec 06 2004
%e A090493 a(5)=19: 5^19 = 19073486328125.
%p A090493 a:= proc(n) local k;
%p A090493    if n = 10^ilog10(n) then return 0 fi;
%p A090493    for k from 1 do
%p A090493      if nops(convert(convert(n^k,base,10),set))=10 then return k fi
%p A090493    od
%p A090493 end proc:
%p A090493 seq(a(n),n=1..100); # _Robert Israel_, Aug 20 2014
%t A090493 Table[If[IntegerQ@ Log10[n], 0, SelectFirst[Range[#, # + 100] &@ Ceiling[9 Log[n, 10]], NoneTrue[DigitCount[n^#], # == 0 &] &]], {n, 71}] (* _Michael De Vlieger_, Sep 06 2017 *)
%o A090493 (PARI) a(n) = if (n == 10^valuation(n, 10), return (0)); k=1; while(#vecsort(digits(n^k),,8)!=10, k++); k; \\ _Michel Marcus_, Aug 20 2014
%o A090493 (Python)
%o A090493 def a(n):
%o A090493   s = str(n)
%o A090493   if n == 1 or (s.count('0')==len(s)-1 and s.startswith('1')):
%o A090493     return 0
%o A090493   k = 1
%o A090493   count = 0
%o A090493   while count != 10:
%o A090493     count = 0
%o A090493     for i in range(10):
%o A090493       if str(n**k).count(str(i)) == 0:
%o A090493         count += 1
%o A090493         break
%o A090493     if count:
%o A090493       k += 1
%o A090493     else:
%o A090493       return k
%o A090493 n = 1
%o A090493 while n < 100:
%o A090493   print(a(n), end=', ')
%o A090493   n += 1
%o A090493 # _Derek Orr_, Aug 20 2014
%Y A090493 Cf. A020665, A062518, A171102.
%Y A090493 Exponents of powers of k that contain all ten decimal digits: A130694 (k=2), A236673 (k=3), A284670 (k=5), A284672 (k=7).
%K A090493 base,nonn
%O A090493 1,2
%A A090493 _Amarnath Murthy_, Dec 03 2003
%E A090493 More terms from _Reinhard Zumkeller_, Dec 06 2004
%E A090493 Corrected a(15), a(17), a(38), a(48), a(56) and a(65). (For each of these terms, the only 1 in n^k is the first digit.) - _Jon E. Schoenfield_, Sep 20 2008