A305941 Smallest power of n having at least one digit 0 (when written in base 10).

1024, 59049, 1024, 390625, 10077696, 2401, 4096, 59049, 10, 161051, 20736, 4826809, 105413504, 50625, 4096, 410338673, 104976, 130321, 20, 4084101, 10648, 148035889, 191102976, 390625, 308915776, 14348907, 17210368, 707281, 30, 887503681, 1024, 1089, 39304, 1500625, 60466176, 50653, 2085136, 90224199, 40

Offset: 2

Author

M. F. Hasler, Jun 19 2018

Keywords

• nonn
• easy
• base

Comments

One would have a(0) = 0 (= 0^1), but a(1) is undefined.

The similar sequence defined as "...exactly one digit 0..." would be ill-defined for all powers of 100, 1001, and others.

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A071531.

Programs

Mathematica

Table[Module[{k=1},While[DigitCount[n^k,10,0]==0,k++];n^k],{n,2,40}] (* Harvey P. Dale, Aug 18 2025 *)

PARI

apply( A305941(n)=for(k=1,oo, vecmin(digits(n^k))||return(n^k)), [2..20])

Formula

a(n) >= n, with equality iff n is in A011540 \ {0} = {10, 20, ..., 100, 101, ...}.