1,1

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. a(7) is itself semiprime. The smallest primes in this sequence are a(3) = 315361 and a(4) = 11667713. What is the next prime?

a(n) = SUM[from i = 1 to n] (semiprime(i))^(semiprime(n-i+1)). a(n) = SUM[from i = 1 to n] (A001358(i))^(A001358(n-i+1)).

a(1) = 256 because semiprime(1)^semiprime(1) = 4^4 = 256.

a(2) = 5392 because prime(1)^prime(2) + prime(2)^prime(1) = 4^6 + 6^4 = 5392.

a(3) = 315361 because 4^9 + 6^6 + 9^4 = 315361.

a(4) = 11667713 = 4^10 + 6^9 + 9^6 + 10^4.

a(5) = 717360537 = 4^14 + 6^10 + 9^9 + 10^6 + 14^4.

a(6) = 83932270482 = 4^15 + 6^14 + 9^10 + 10^9 + 14^6 + 15^4.

a(7) = 27775696582531 = 4^21 + 6^15 + 9^14 + 10^10 + 14^9 + 15^6 + 21^4.

a(8) = 22260761742531649 = 4^22 + 6^21 + 9^15 + 10^14 + 14^10 + 15^9 + 21^6 + 22^4.

a(9) = 109563850113131234720 = 4^25 + 6^22 + 9^21 + 10^15 + 14^14 + 15^10 + 21^9 + 22^6 + 25^4.

Cf. A001358, A005408, A113122, A113153, A113154.

Sequence in context: A074151 A016804 A115111 this_sequence A077072 A128698 A016900

Adjacent sequences: A113170 A113171 A113172 this_sequence A113174 A113175 A113176

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 07 2006