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A085298 a(n) is the smallest exponent x such that prime(n)^x when reversed is a prime.

%I A085298 #16 Sep 04 2019 16:00:48
%S A085298 1,1,1,1,1,1,1,2,8,7,1,1,2,5,15,10,12,4,39,1,1,1,11,2,1,1,10,1,23,1,5,
%T A085298 1,243,2,1,1,1,23,1,34,1,1,1,2,58,1,3,9,166,17,68,8,8,3,7,5,5,2,2,2,
%U A085298 61,11,97,1,1,10,2,1,1,41,1,1,66,1,5,1,1,2,2,8,40,2,8,19,2,2,723
%N A085298 a(n) is the smallest exponent x such that prime(n)^x when reversed is a prime.
%C A085298 It is conjectured that for every n such exponent exists.
%H A085298 Giovanni Resta, <a href="/A085298/b085298.txt">Table of n, a(n) for n = 1..100</a>
%F A085298 a(n) = Min{x; reversed(prime(n)^x) is a prime}.
%e A085298 a(n)=1 means that rev(prime(n)) is prime i.e. prime(n) is in A007500;
%e A085298 a(n)=2 means that rev(prime(n)^2) is prime but rev(prime(n)) is not, like n=8:p=19 and 91 is not a prime but rev[19^2]=rev[361]=163 is a prime;
%e A085298 For n, the first k exponent providing rev(prime(n)^k) prime can be quite large, like at n=87: rev(p(87)^723)=rev(449^723) is the first [probably] prime has 1918 decimal digits: 948......573.
%p A085298 a:= proc(n) local k, p; p:= ithprime(n); for k while not isprime((s->
%p A085298       parse(cat(seq(s[-i], i=1..length(s)))))(""||(p^k))) do od; k
%p A085298     end:
%p A085298 seq(a(n), n=1..50);  # _Alois P. Heinz_, Sep 04 2019
%t A085298 a[n_] := Block[{k = 1}, While[! PrimeQ@ FromDigits@ Reverse@ IntegerDigits[ Prime[n]^k], k++]; k]; Array[a, 87] (* _Giovanni Resta_, Sep 04 2019 *)
%o A085298 (PARI) a(n) = {my(x=1, p=prime(n)); while (!ispseudoprime(fromdigits(Vecrev(digits(p^x)))), x++); x;} \\ _Michel Marcus_, Sep 04 2019
%Y A085298 Cf. A000040, A057708, A058993, A056994, A059695, A003459, A007500, A055387, A061461, A068652.
%K A085298 base,nonn
%O A085298 1,8
%A A085298 _Labos Elemer_, Jun 24 2003