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A259084 a(n) = largest k such that the decimal representation of prime(n)^k does not contain the digit 0.

%I A259084 #16 Jun 19 2015 16:34:00
%S A259084 86,68,58,35,41,14,27,44,10,14,16,16,9,10,8,7,14,16,14,8,6,9,4,23,8,0,
%T A259084 14,10,12,10,6,14,5,8,5,13,7,16,7,17,6,3,9,9,16,7,12,11,4,13,7,16,8,9,
%U A259084 3,10,4,9,6,4,5,13,3,12,7,9,6,8,4,39,13,12,10,4
%N A259084 a(n) = largest k such that the decimal representation of prime(n)^k does not contain the digit 0.
%C A259084 These values are only conjectural.
%C A259084 a(n) = 0 if prime(n) is in A062800. - _Robert Israel_, Jun 19 2015
%H A259084 Hiroaki Yamanouchi, <a href="/A259084/b259084.txt">Table of n, a(n) for n = 1..500</a>
%H A259084 Popular Computing (Calabasas, CA), <a href="/A094776/a094776.jpg">Two Tables</a>, Vol. 1, (No. 9, Dec 1973), page PC9-16.
%e A259084 a(1)=86 because 2^86 = 77371252455336267181195264 is conjectured to be the highest power of 2 that doesn't contain the digit 0.
%p A259084 N:= 100: K:= 100:  # to get a(1) to a(N), searching up to k = K
%p A259084 for n from 1 to N do
%p A259084   p:= ithprime(n);
%p A259084   A[n]:= 0;
%p A259084   for k from 1 to K do
%p A259084     if not has(convert(p^k,base,10),0) then
%p A259084        A[n]:= k
%p A259084     fi
%p A259084   od
%p A259084 od:
%p A259084 seq(A[n],n=1..N); # _Robert Israel_, Jun 19 2015
%Y A259084 Cf. A062800, A094776, A259081-A259086.
%K A259084 nonn,base
%O A259084 1,1
%A A259084 _N. J. A. Sloane_, Jun 18 2015
%E A259084 a(14)-a(57) from _Hiroaki Yamanouchi_, Jun 19 2015