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%I A062518 #44 Oct 04 2021 20:33:14
%S A062518 0,168,106,84,65,64,61,56,53,0,41,51,37,34,34,42,27,25,44,168,29,24,
%T A062518 50,23,29,31,28,28,45,106,28,18,24,34,18,32,25,17,41,84,23,19,20,29,
%U A062518 39,32,15,29,16,65,29,29,30,18,17,33,19,31,27,64,26,19,24,28,17,15,21,25,13
%N A062518 Conjectural largest exponent k such that n^k does not contain all of the digits 0 through 9 (in decimal notation) or 0 if no such k exists (for example if n is a power of 10).
%C A062518 I do not know how many of these terms have been proved to be correct. - _N. J. A. Sloane_
%C A062518 In particular, are the powers of 10 the only n with a(n) = 0?
%C A062518 Note that a(10n) = a(n) unless n^a(n) contains no 0 (i.e., a(n) = A020665(n)), in which case a(10n) < a(n). - _Christopher J. Smyth_, Aug 20 2014
%C A062518 From _Robert G. Wilson v_, Aug 22 2021: (Start)
%C A062518 Conjectured first occurrence of k for k >= 0: 1, 156224, 22148, 7342, 3376, 861, 609, 477, 295, 152, 153, 149, 138, 69, 139, 47, 49, 38, 32, 42, 43, 67, 92, 24, 22, 18, 61, 17, 27, 21, 53, 26, 36, 56, 14, 190, 271, 13, 110, 45, ?40?, 11, 16, ?43?, 19, 29, ..., .
%C A062518 Other integers which satisfy a(n) = 0 are 1023458769, 1023458967, 1023467895, 1023469875, 1023475986, 1023478695, .... These are all members of A171102.
%C A062518 (End)
%F A062518 a(n^e) <= a(n)/e. - _Robert G. Wilson v_, Oct 02 2021
%e A062518 a(11) = 41 as 11^41 = 4978518112499354698647829163838661251242411 is the conjectural highest power of 11 not containing all ten digits.
%e A062518 a(110) = 38 as 110^38 does not contain the digit 2, while, conjecturally, all higher powers of 110 contain all ten digits. - _Christopher J. Smyth_, Aug 20 2014
%Y A062518 Cf. A090493, A020665, A171102.
%K A062518 base,nonn
%O A062518 1,2
%A A062518 _Robert G. Wilson v_, Jun 24 2001
%E A062518 Definition corrected by _Christopher J. Smyth_, Aug 20 2014.

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