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

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base

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

Examples

			Here is 3^68, conjecturally the largest power of 3 that does not contain a zero: 278128389443693511257285776231761. - _N. J. A. Sloane_, Feb 10 2023
		

Links

• 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

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.

Programs

Magma

[n: n in [0..500] | not 0 in Intseq(3^n) ]; // Vincenzo Librandi, Oct 19 2012

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 *)

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

Extensions

Initial term 0 added by Vincenzo Librandi, Oct 19 2012