A030700 - OEIS

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A030700

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

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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OFFSET

1,3

COMMENTS

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

LINKS

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

EXAMPLE

Here is 3^68, conjecturally the largest power of 3 that does not contain a zero:

278128389443693511257285776231761. - N. J. A. Sloane, Feb 10 2023

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein

EXTENSIONS

Initial term 0 added by Vincenzo Librandi, Oct 19 2012

STATUS

approved