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A030700
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Decimal expansion of 3^n contains no zeros (probably finite).
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36
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 19, 23, 24, 26, 27, 28, 31, 34, 68
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history;
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OFFSET
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1,3
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COMMENTS
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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
See A238939(n) = 3^a(n) for the actual powers. - M. F. Hasler, Mar 08 2014
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LINKS
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Table of n, a(n) for n=1..23.
M. F. Hasler, Zeroless powers, OEIS Wiki, Mar 07 2014
W. Schneider, NoZeros: Powers n^k without Digit Zero [Cached copy]
Eric Weisstein's World of Mathematics, Zero
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EXAMPLE
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Here is 3^68, conjecturally the largest power of 3 that does not contain a zero:
278128389443693511257285776231761. - N. J. A. Sloane, Feb 10 2023
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MATHEMATICA
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Do[If[Union[RealDigits[3^n][[1]]][[1]]!=0, Print[n]], {n, 0, 10000}] (* Vincenzo Librandi, Oct 19 2012 *)
Select[Range[0, 70], DigitCount[3^#, 10, 0]==0&] (* Harvey P. Dale, Feb 06 2019 *)
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PROG
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(Magma) [n: n in [0..500] | not 0 in Intseq(3^n) ]; // Vincenzo Librandi, Oct 19 2012
(PARI) is_A030700(n)=vecmin(digits(3^n)) \\ M. F. Hasler, Mar 07 2014
(PARI) A030700=select( is_A030700, [0..199]) \\ M. F. Hasler, Jun 14 2018
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CROSSREFS
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For the zeroless numbers (powers x^n), see A238938, A238939, A238940, A195948, A238936, A195908, A195946, A195945, A195942, A195943, A103662.
For the corresponding exponents, see A007377, A030700 (this), A030701, A008839, A030702, A030703, A030704, A030705, A030706, A195944.
For other related sequences, see A052382, A027870, A102483, A103663.
Sequence in context: A325097 A333126 A330697 * A305933 A105208 A074779
Adjacent sequences: A030697 A030698 A030699 * A030701 A030702 A030703
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KEYWORD
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nonn,base
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Initial term 0 added by Vincenzo Librandi, Oct 19 2012
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STATUS
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approved
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