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A103663 Smallest integer base x > 1 such that x^n has no digit 0 in its decimal representation, or 0 if no such x exists. 16

%I #13 Mar 11 2014 18:03:25

%S 2,2,2,2,2,2,2,2,2,2,5,3,3,2,2,2,2,4,2,2,12,381,22,3,2,2,3,2,2,6,5,2,

%T 2,2,2,2,2,2,4,2,0,11,0,4,6,0,0,0,0,2,0,2,0,0,0,0,0,0,5,0,0,0,0,0,0,0,

%U 0,2,3,0,0,0,2,0,0,0,2,2,0,0,0,2,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Smallest integer base x > 1 such that x^n has no digit 0 in its decimal representation, or 0 if no such x exists.

%C Bases associated with A103662. [Corrected by _M. F. Hasler_, Mar 09 2014]

%C Zero values are conjectural. a(40) was checked up to 10^9 by _Joshua Zucker_. All other zero values were checked up to 10^5 by _David Wasserman_.

%e a(10) = 5 because 5^10 is the smallest 10th power containing no zero in its decimal representation (2^10 = 1024, 3^10 = 59049, 4^10 = 1048576).

%Y Cf. A103662 = smallest power x^n with integer x>1 that has no digit 0 in its decimal representation.

%Y A007377 gives n such that a(n) = 2. Cf. A008839, A030700-A030706.

%K base,nonn

%O 0,1

%A _Hugo Pfoertner_, Feb 28 2005

%E a(21) = 381 found by _Joshua Zucker_

%E More terms from _David Wasserman_, Apr 17 2008

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Last modified April 25 05:18 EDT 2024. Contains 371964 sequences. (Running on oeis4.)