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A085324 a(n) is the least exponent so that reverse(n^a(n)) is a prime number. a(n)=0 if no such exponent exists, namely when e.g., n = 3k or n = 11k, k > 1.

%I A085324 #19 Mar 27 2020 06:30:48
%S A085324 0,1,1,2,1,0,1,8,0,0,1,0,1,1,0,1,1,0,2,1,0,0,8,0,13,47,0,2,7,0,1,1,0,
%T A085324 1,1,0,1,1,0,2,2,0,5,0,0,22,15,0,6,1,0,3,10,0,0,143,0,88,12,0,4,2,0,4,
%U A085324 8,0,39,83,0,1,1,0,1,1,0,1,0,0,1,8,0,6,11,0,2,28,0,0,2,0,1,1,0,292,1,0,1,1
%N A085324 a(n) is the least exponent so that reverse(n^a(n)) is a prime number. a(n)=0 if no such exponent exists, namely when e.g., n = 3k or n = 11k, k > 1.
%C A085324 a(k) = 1 for k in A095179. - _Michel Marcus_, Apr 09 2018
%H A085324 Robert Israel, <a href="/A085324/b085324.txt">Table of n, a(n) for n = 1..202</a>
%F A085324 a(3k) = a(11k) = 0 for k > 1 because reversion does not make a prime from any of their powers.
%e A085324 For n=46, a(46)=22 means that reversion of 46^22 gives a prime: 6100744433653913942689966672393877083.
%p A085324 Rev:= proc(n) local L;
%p A085324 L:= convert(n,base,10);
%p A085324 add(L[-i]*10^(i-1),i=1..nops(L))
%p A085324 end proc:
%p A085324 f:= proc(n) local k;
%p A085324   if igcd(n,33) <> 1  then return 0 fi;
%p A085324   if n mod 10 = 0 then return procname(n/10) fi;
%p A085324   for k from 1 do if isprime(Rev(n^k)) then return k fi od:
%p A085324 end proc:
%p A085324 f(1):= 0: f(3):= 1; f(11):= 1;
%p A085324 map(f, [$1..100]); # _Robert Israel_, Apr 09 2018
%t A085324 nd[x_, y_] := 10*x+y; tn[x_] := Fold[nd, 0, x]; bac[x_] := tn[Reverse[IntegerDigits[x]]] t={list without 3k and 11k numbers}; le=Length[t]; Table[f=1; Do[s=bac[Part[t, n]^k]; If[PrimeQ[s]&&Equal[f, 1], Print[{k, Part[t, n], s}]; f=0], {k, 1, 300}], {n, 1, le}]
%Y A085324 Cf. A085325, A085298, A085299, A085300.
%K A085324 base,nonn
%O A085324 1,4
%A A085324 _Labos Elemer_, Jul 02 2003