cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A305941 #20 Aug 18 2025 12:16:06
%S A305941 1024,59049,1024,390625,10077696,2401,4096,59049,10,161051,20736,
%T A305941 4826809,105413504,50625,4096,410338673,104976,130321,20,4084101,
%U A305941 10648,148035889,191102976,390625,308915776,14348907,17210368,707281,30,887503681,1024,1089,39304,1500625,60466176,50653,2085136,90224199,40
%N A305941 Smallest power of n having at least one digit 0 (when written in base 10).
%C A305941 One would have a(0) = 0 (= 0^1), but a(1) is undefined.
%C A305941 The similar sequence defined as "...exactly one digit 0..." would be ill-defined for all powers of 100, 1001, and others.
%H A305941 Alois P. Heinz, <a href="/A305941/b305941.txt">Table of n, a(n) for n = 2..10000</a>
%F A305941 a(n) >= n, with equality iff n is in A011540 \ {0} = {10, 20, ..., 100, 101, ...}.
%t A305941 Table[Module[{k=1},While[DigitCount[n^k,10,0]==0,k++];n^k],{n,2,40}] (* _Harvey P. Dale_, Aug 18 2025 *)
%o A305941 (PARI) apply( A305941(n)=for(k=1,oo, vecmin(digits(n^k))||return(n^k)), [2..20])
%Y A305941 Cf. A071531.
%K A305941 nonn,easy,base
%O A305941 2,1
%A A305941 _M. F. Hasler_, Jun 19 2018