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.
%I A124648 #18 Jan 14 2024 11:49:50
%S A124648 1,2,3,5,6,68,76,3944,15483
%N A124648 Numbers n such that n^i (i=1..7) are all zeroless.
%C A124648 No other terms < 10^8. - _Michel Marcus_, Oct 11 2013
%C A124648 No other terms < 10^13. - _Charles R Greathouse IV_, Oct 14 2013
%C A124648 Subsequence of A253647, the analog with i <= 6 instead of 7. Conjectured to be finite. - _M. F. Hasler_, Jan 07 2015
%C A124648 a(10) > 3.3*10^16, if it exists. - _Giovanni Resta_, Sep 06 2018
%e A124648 15483^i (i=1..7) = 15483, 239723289, 3711635683587, 57467255288977521, 889765513639238957643, 13776239447676336781186569, 213297515368372722383111647827 all zeroless.
%t A124648 Select[Range[10^6], FreeQ[Union[IntegerDigits[ # ],IntegerDigits[ #^2],IntegerDigits[ #^3],IntegerDigits[ #^4],IntegerDigits[ #^5],IntegerDigits[ #^6],IntegerDigits[ #^7]],0]&]
%t A124648 Select[Range[15500],FreeQ[Flatten[IntegerDigits/@(#^Range[7])],0]&] (* _Harvey P. Dale_, Jan 14 2024 *)
%o A124648 (PARI) isok(n) = {for (i = 1, 7, if (! vecmin(digits(n^i)), return (0));); return (1);} \\ _Michel Marcus_, Oct 11 2013
%o A124648 (PARI) \\ Script for checking for large (> 10^9) members:
%o A124648 is(n)=for(i=1,7,if(vecmin(digits(n^i))==0, return(0))); 1
%o A124648 bad(n,d)=for(k=1,d,if(n%10==0,return(1));n\=10);0
%o A124648 good7(n,d)=my(t=1);for(i=1,7,if(bad(lift(t*=n),d),return(0)));1
%o A124648 left(d)=my(v=List(),m=10^d);for(i=0,10^d-1, if(good7(Mod(i,m),d), listput(v,i)));Vec(v)
%o A124648 diff(v)=vector(#v-1,i,v[i+1]-v[i])
%o A124648 L=left(9);D=diff(concat(L,10^9+L[1]));forstep(n=L[1],1e12,D, if(is(n),print(n))) \\ _Charles R Greathouse IV_, Oct 14 2013
%Y A124648 Cf. A253647, A104264, A124649.
%K A124648 nonn,base,more
%O A124648 1,2
%A A124648 _Zak Seidov_, Dec 22 2006