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

1,3

Comments

Probably 58 is last term.

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

Links

Table of n, a(n) for n=1..16.

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 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

Mathematica

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

Prog

(Magma) [ n: n in [0..500] | not 0 in Intseq(5^n) ]; // Vincenzo Librandi Oct 19 2012
(PARI) for(n=0, 99, vecmin(digits(5^n))&& print1(n", ")) \\ M. F. Hasler, Mar 07 2014

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.

Sequence in context: A117729 A073726 A194125 * A305925 A039226 A277882

Adjacent sequences: A008836 A008837 A008838 * A008840 A008841 A008842

Keyword

nonn,base

Author

Olivier Gérard

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.

Status

approved