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A124648 Numbers n such that n^i (i=1..7) are all zeroless. 6

%I

%S 1,2,3,5,6,68,76,3944,15483

%N Numbers n such that n^i (i=1..7) are all zeroless.

%C No other terms < 10^8. - _Michel Marcus_, Oct 11 2013

%C No other terms < 10^13. - _Charles R Greathouse IV_, Oct 14 2013

%C Subsequence of A253647, the analog with i <= 6 instead of 7. Conjectured to be finite. - _M. F. Hasler_, Jan 07 2015

%C a(10) > 3.3*10^16, if it exists. - _Giovanni Resta_, Sep 06 2018

%e 15483^i (i=1..7) = 15483, 239723289, 3711635683587, 57467255288977521, 889765513639238957643, 13776239447676336781186569, 213297515368372722383111647827 all zeroless.

%t Select[Range[10^6], FreeQ[Union[IntegerDigits[ # ],IntegerDigits[ #^2],IntegerDigits[ #^3],IntegerDigits[ #^4],IntegerDigits[ #^5],IntegerDigits[ #^6],IntegerDigits[ #^7]],0]&]

%o (PARI) isok(n) = {for (i = 1, 7, if (! vecmin(digits(n^i)), return (0));); return (1);} \\ _Michel Marcus_, Oct 11 2013

%o (PARI) \\ Script for checking for large (> 10^9) members:

%o is(n)=for(i=1,7,if(vecmin(digits(n^i))==0, return(0))); 1

%o bad(n,d)=for(k=1,d,if(n%10==0,return(1));n\=10);0

%o good7(n,d)=my(t=1);for(i=1,7,if(bad(lift(t*=n),d),return(0)));1

%o 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 diff(v)=vector(#v-1,i,v[i+1]-v[i])

%o 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 Cf. A253647, A104264, A124649.

%K nonn,base,more

%O 1,2

%A _Zak Seidov_, Dec 22 2006

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Last modified July 26 08:42 EDT 2021. Contains 346294 sequences. (Running on oeis4.)