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Numbers n such that n^i (i=1..8) are all zeroless.
6

%I #9 Sep 27 2023 14:11:35

%S 1,2,3,6,68

%N Numbers n such that n^i (i=1..8) are all zeroless.

%C No other terms < 10^6. Is the sequence finite?

%C Subsequence of A124648. No other terms below 10^8. - _Michel Marcus_, Oct 11 2013

%C a(6) > 3.3*10^16, if it exists. - _Giovanni Resta_, Sep 07 2018

%e 68^i (i=1..8)= 68, 4624, 314432, 21381376, 1453933568, 98867482624, 6722988818432, 457163239653376 all zeroless.

%t zLessQ[n_]:=AllTrue[n^Range[8],FreeQ[IntegerDigits[#],0]&]; Select[Range[70],zLessQ] (* _Harvey P. Dale_, Sep 27 2023 *)

%o (PARI) isok(n) = {for (i = 1, 8, if (! vecmin(digits(n^i)), return (0));); return (1);} \\ _Michel Marcus_, Oct 11 2013

%Y Cf. A104264.

%K nonn,base,more

%O 1,2

%A _Zak Seidov_, Dec 22 2006