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A030700 Decimal expansion of 3^n contains no zeros (probably finite).

%I A030700 #51 Feb 16 2025 08:32:35
%S A030700 0,1,2,3,4,5,6,7,8,9,11,12,13,14,19,23,24,26,27,28,31,34,68
%N A030700 Decimal expansion of 3^n contains no zeros (probably finite).
%C A030700 See A007377 for the analog for 2^n (final term seems to be 86), A008839 for 5^n (final term seems to be 58), and others listed in cross-references. - _M. F. Hasler_, Mar 07 2014
%C A030700 See A238939(n) = 3^a(n) for the actual powers. - _M. F. Hasler_, Mar 08 2014
%H A030700 M. F. Hasler, <a href="https://oeis.org/wiki/Zeroless_powers">Zeroless powers</a>, OEIS Wiki, Mar 07 2014
%H A030700 W. Schneider, <a href="/A007496/a007496.html">NoZeros: Powers n^k without Digit Zero</a> [Cached copy]
%H A030700 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Zero.html">Zero</a>
%e A030700 Here is 3^68, conjecturally the largest power of 3 that does not contain a zero: 278128389443693511257285776231761. - _N. J. A. Sloane_, Feb 10 2023
%t A030700 Do[If[Union[RealDigits[3^n][[1]]][[1]]!=0, Print[n]], {n, 0,10000}] (* _Vincenzo Librandi_, Oct 19 2012 *)
%t A030700 Select[Range[0,70],DigitCount[3^#,10,0]==0&] (* _Harvey P. Dale_, Feb 06 2019 *)
%o A030700 (Magma) [n: n in [0..500] | not 0 in Intseq(3^n) ]; // _Vincenzo Librandi_, Oct 19 2012
%o A030700 (PARI) is_A030700(n)=vecmin(digits(3^n)) \\ _M. F. Hasler_, Mar 07 2014
%o A030700 (PARI) A030700=select( is_A030700, [0..199]) \\ _M. F. Hasler_, Jun 14 2018
%Y A030700 For the zeroless numbers (powers x^n), see A238938, A238939, A238940, A195948, A238936, A195908, A195946, A195945, A195942, A195943, A103662.
%Y A030700 For the corresponding exponents, see A007377, A030700 (this), A030701, A008839, A030702, A030703, A030704, A030705, A030706, A195944.
%Y A030700 For other related sequences, see A052382, A027870, A102483, A103663.
%K A030700 nonn,base
%O A030700 1,3
%A A030700 _Eric W. Weisstein_
%E A030700 Initial term 0 added by _Vincenzo Librandi_, Oct 19 2012