A008839 Numbers k such that the decimal expansion of 5^k contains no zeros.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 17, 18, 30, 33, 58

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• base

Comments

Probably 58 is last term.

Searched for k up to 10^10. - David Radcliffe, Dec 27 2015

Examples

			Here is 5^58, conjecturally the largest power of 5 that does not contain a 0:
34694469519536141888238489627838134765625. - _N. J. A. Sloane_, Feb 10 2023, corrected by _Patrick De Geest_, Jun 09 2024
		

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

Cf. A000351 (5^n).

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, A008839, A030700, A030701, A008839, A030702, A030703, A030704, A030705, A030706, A195944.

For other related sequences, see A305925, A052382, A027870, A102483, A103663.

Programs

Magma

[ n: n in [0..500] | not 0 in Intseq(5^n) ]; // Vincenzo Librandi Oct 19 2012

Mathematica

Do[ If[ Union[ RealDigits[ 5^n ][[1]]] [[1]] != 0, Print[ n ]], {n, 0, 25000}]

PARI

for(n=0,99,vecmin(digits(5^n))&& print1(n",")) \\ M. F. Hasler, Mar 07 2014

Extensions

Definition corrected and initial term 0 added by M. F. Hasler, Sep 25 2011

Further edits by M. F. Hasler, Mar 08 2014

Keyword:fini removed by Jianing Song, Jan 28 2023 as finiteness is only conjectured.