%I A113231
%S A113231 1,4,34,956,106721,75818480,490656737694,22960404169011552,
%T A113231 7141530219670856270919,20319415706020976355219258316,
%U A113231 1104797870481014132439711155738991604
%N A113231 Ascending descending base exponent transform of triangular numbers (A000217).
%C A113231 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. Since 
               the parity of the triangular numbers cycles odd, odd, even, even; 
               the parity of this sequence cycles odd, even, even, even. The smallest 
               prime in this sequence is a(5) = 127601. What is the next prime? 
               What is the first triangular value?
%F A113231 a(n) = SUM[from i = 1 to n] (T(i))^(T(n-i+1)). a(n) = SUM[from i = 1 
               to n] ((i*(i+1)/2))^((n-i+1)*(n-i+2)/2). a(n) = SUM[from i = 1 to 
               n] (A000217(i))^(A000217(n-i+1)).
%e A113231 a(1) = 1 because T(1)^T(1) = 1^1 = 1.
%e A113231 a(2) = 4 because T(1)^T(2) + T(2)^T(1) = 1^3 + 3^1 = 4.
%e A113231 a(3) = 34 = 1^6 + 3^3 + 6^1.
%e A113231 a(4) = 956 = 1^10 + 3^6 + 6^3 + 10^1.
%e A113231 a(5) = 106721 = 1^15 + 3^10 + 6^6 + 10^3 + 15^1.
%e A113231 a(6) = 75818480 = 1^21 + 3^15 + 6^10 + 10^6 + 15^3 + 21^1.
%e A113231 a(7) = 490656737694 = 1^28 + 3^21 + 6^15 + 10^10 + 15^6 + 21^3 + 28^1.
%e A113231 a(8) = 22960404169011552 = 1^36 + 3^28 + 6^21 + 10^15 + 15^10 + 21^6 
               + 28^3 + 36^1.
%e A113231 a(9) = 7141530219670856270919 = 1^45 + 3^36 + 6^28 + 10^21 + 15^15 + 
               21^10 + 28^6 + 36^3 + 45^1.
%Y A113231 Cf. A000217, A005408, A113122, A113153, A113154.
%Y A113231 Sequence in context: A030243 A088077 A162079 this_sequence A055621 A000860 
               A027681
%Y A113231 Adjacent sequences: A113228 A113229 A113230 this_sequence A113232 A113233 
               A113234
%K A113231 easy,nonn
%O A113231 1,2
%A A113231 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 07 2006