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A103662 Smallest power with base>1 and exponent n whose decimal representation doesn't contain the digit 0.

%I A103662 #24 Jan 28 2023 14:01:12
%S A103662 1,2,4,8,16,32,64,128,256,512,9765625,177147,531441,8192,16384,32768,
%T A103662 65536,17179869184,262144,524288,3833759992447475122176,
%U A103662 1582794342217312156827221746448942623537121214738891981,341427877364219557396646723584,94143178827,16777216
%N A103662 Smallest power with base>1 and exponent n whose decimal representation doesn't contain the digit 0.
%C A103662 For statistical reasons it is conjectured that the sequence is finite.
%C A103662 a(40), if it exists, is not known.
%C A103662 From _M. F. Hasler_, Mar 08 2014 (Start):
%C A103662 Finite means here that for some n, no such power > 1 exists. This might be the case already for n=40. Alternatively, the sequence might be defined for all n by letting a(n)=1 if no larger power exists. Then a(n)=n^A103663(n) for all n.
%C A103662 Differs from A238938 from n=10 on. See the OEIS wiki page for further information. (End)
%H A103662 Michel Marcus, <a href="/A103662/b103662.txt">Table of n, a(n) for n = 0..39</a>
%H A103662 M. F. Hasler, <a href="https://oeis.org/wiki/Zeroless_powers">Zeroless powers</a>, OEIS wiki, Mar 07 2014
%F A103662 a(n) = A103663(n)^n. - _M. F. Hasler_, Mar 08 2014
%e A103662 base / exponent n / base^exponent
%e A103662 2 1 2
%e A103662 2 2 4
%e A103662 2 3 8
%e A103662 2 4 16
%e A103662 2 5 32
%e A103662 2 6 64
%e A103662 2 7 128
%e A103662 2 8 256
%e A103662 2 9 512
%e A103662 5 10 9765625
%e A103662 3 11 177147
%e A103662 3 12 531441
%e A103662 2 13 8192
%e A103662 2 14 16384
%e A103662 2 15 32768
%e A103662 2 16 65536
%e A103662 4 17 17179869184
%e A103662 2 18 262144
%e A103662 2 19 524288
%e A103662 12 20 3833759992447475122176
%e A103662 381 21 1582794342217312156827221746448942623537121214738891981
%e A103662 22 22 341427877364219557396646723584
%e A103662 3 23 94143178827
%e A103662 ...
%e A103662 a(10)=9765625 because 5^10 is the smallest 10th power containing no zero in its decimal representation (2^10=1024, 3^10=59049, 4^10=1048576).
%o A103662 (PARI) A103662(n)=for(b=2,9e9,vecmin(digits(b^n))&&return(b^n)) \\ _M. F. Hasler_, Mar 08 2014
%Y A103662 Cf. A103663 = smallest bases x such that x^n has a zero-less decimal representation.
%K A103662 nonn,base
%O A103662 0,2
%A A103662 _Hugo Pfoertner_, Feb 28 2005
%E A103662 a(21)=381^21 found by _Joshua Zucker_.
%E A103662 Edited by _Charles R Greathouse IV_, Aug 03 2010
%E A103662 Keyword:fini removed by _Jianing Song_, Jan 28 2023 as finiteness is only conjectured.