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

2,1

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A071531.

Sequence in context: A321834 A182681 A182682 * A351198 A195250 A016901

Adjacent sequences: A305938 A305939 A305940 * A305942 A305943 A305944

Keyword

nonn,easy,base

Author

M. F. Hasler, Jun 19 2018

Status

approved