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A124648 Numbers n such that n^i (i=1..7) are all zeroless. 6
1, 2, 3, 5, 6, 68, 76, 3944, 15483 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..9.

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]&]

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

Cf. A253647, A104264, A124649.

Sequence in context: A076384 A261579 A270517 * A093339 A113566 A020775

Adjacent sequences:  A124645 A124646 A124647 * A124649 A124650 A124651

KEYWORD

nonn,base,more

AUTHOR

Zak Seidov, Dec 22 2006

STATUS

approved

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Last modified June 16 04:26 EDT 2021. Contains 345055 sequences. (Running on oeis4.)