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A124648
Numbers n such that n^i (i=1..7) are all zeroless.
7
1, 2, 3, 5, 6, 68, 76, 3944, 15483
OFFSET
1,2
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
EXAMPLE
15483^i (i=1..7) = 15483, 239723289, 3711635683587, 57467255288977521, 889765513639238957643, 13776239447676336781186569, 213297515368372722383111647827 all zeroless.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Zak Seidov, Dec 22 2006
STATUS
approved

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Last modified September 19 23:07 EDT 2024. Contains 376015 sequences. (Running on oeis4.)