%I A113336
%S A113336 2,1,6,6,18,12,18,42
%N A113336 Least integers, starting with 2, so ascending descending base exponent 
               transforms all prime.
%C A113336 This is the second sequence submitted as a solution to an "ascending 
               descending base exponent transform inverse problem" where the sequence 
               is iteratively defined such that the transform meets a constraint. 
               The sequence is probably infinite, but it is hard to characterize 
               the asymptotic cost of adding an n-th term (the 9th terms is at least 
               250). A003101 is the ascending descending base exponent transform 
               of natural numbers A000027. The ascending descending base exponent 
               transform applied to the Fibonacci numbers is A113122; applied to 
               the tribonacci numbers is A113153; applied to the Lucas numbers is 
               A113154.
%F A113336 a(1) = 2. For n>1: a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(n-i+1)) 
               is prime}.
%e A113336 a(1) = 2 by definition.
%e A113336 a(2) = 1 because 1 is the min such that 2^a(2) + a(2)^2 is prime (p=3).
%e A113336 a(3) = 6 because 6 is the min such that 2^a(3) + 1^1 + a(3)^2 is prime 
               (2^6 + 1^1 + 6^1 = 101).
%e A113336 a(4) = 6 because 2^6 + 1^6 + 6^1 + 6^2 = 107 is prime.
%e A113336 a(5) = 18 because 2^18 + 1^6 + 6^6 + 6^1 + 18^2 = 309131 is prime.
%e A113336 a(6) = 12 because 2^12 + 1^18 + 6^6 + 6^6 + 18^1 + 12^2 = 97571 is prime.
%e A113336 a(7) = 18 because 2^18 + 1^12 + 6^18 + 6^6 + 18^6 + 12^1 + 18^2 = 101559990989777 
               is prime.
%e A113336 a(8) = 42 because 2^42 + 1^18 + 6^12 + 6^18 + 18^6 + 12^6 + 18^1 + 42^2 
               = 105960216961847 is prime.
%e A113336 a(9) > 250.
%Y A113336 Cf. A000040, A005408, A113122, A113153, A113154.
%Y A113336 Sequence in context: A117753 A145883 A062820 this_sequence A113979 A053442 
               A019082
%Y A113336 Adjacent sequences: A113333 A113334 A113335 this_sequence A113337 A113338 
               A113339
%K A113336 easy,nonn
%O A113336 1,1
%A A113336 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 07 2006