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

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

Offset: 1

Author

Zak Seidov, Dec 22 2006

Keywords

• nonn
• base
• more

Comments

No other terms < 10^8. - Michel Marcus, Oct 11 2013

No other terms < 10^13. - Charles R Greathouse IV, Oct 14 2013

Subsequence of A253647, the analog with i <= 6 instead of 7. Conjectured to be finite. - M. F. Hasler, Jan 07 2015

a(10) > 3.3*10^16, if it exists. - Giovanni Resta, Sep 06 2018

Examples

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

Crossrefs

Cf. A253647, A104264, A124649.

Programs

Mathematica

Select[Range[10^6], FreeQ[Union[IntegerDigits[ # ],IntegerDigits[ #^2],IntegerDigits[ #^3],IntegerDigits[ #^4],IntegerDigits[ #^5],IntegerDigits[ #^6],IntegerDigits[ #^7]],0]&]
Select[Range[15500],FreeQ[Flatten[IntegerDigits/@(#^Range[7])],0]&] (* Harvey P. Dale, Jan 14 2024 *)

PARI

isok(n) = {for (i = 1, 7, if (! vecmin(digits(n^i)), return (0));); return (1);} \\ Michel Marcus, Oct 11 2013

PARI

\\ Script for checking for large (> 10^9) members:
is(n)=for(i=1,7,if(vecmin(digits(n^i))==0, return(0))); 1
bad(n,d)=for(k=1,d,if(n%10==0,return(1));n\=10);0
good7(n,d)=my(t=1);for(i=1,7,if(bad(lift(t*=n),d),return(0)));1
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)
diff(v)=vector(#v-1,i,v[i+1]-v[i])
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