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. The parity of this sequence cycles even, odd, even, odd... There is no nontrivial integer fixed point of the transform. The smallest prime in this sequence is a(12) = 2^37 + 3^31 + 5^29 + 7^23 + 11^19 + 13^17 + 17^13 + 19^11 + 23^7 + 29^5 + 31^3 + 37^2 = 283453407513524913023. What is the next prime?

a(n) = SUM[from i = 1 to n] (prime(i))^(Prime(n-i+1)). a(n) = SUM[from i = 1 to n] (A000040(i))^(A000040(n-i+1)).

a(1) = 4 because prime(1)^prime(1) = 2^2 = 4.

a(2) = 17 because prime(1)^prime(2) + prime(2)^prime(1) = 2^3 + 3^2 = 17.

a(3) = 84 because 2^5 + 3^3 + 5^2 = 84.

a(4) = 545 = 2^7 + 3^5 + 5^3 + 7^2.

a(5) = 7824 = 2^11 + 3^7 + 5^5 + 7^3 + 11^2.

a(6) = 281771 = 2^13 + 3^11 + 5^7 + 7^5 + 11^3 + 13^2.

a(7) = 51540600 = 2^17 + 3^13 + 5^11 + 7^7 + 11^5 + 13^3 + 17^2.

a(8) = 3347558057 = 2^19 + 3^17 + 5^13 + 7^11 + 11^7 + 13^5 + 17^3 + 19^2.

a(9) = 1146374959980 = 2^23 + 3^19 + 5^17 + 7^13 + 11^11 + 13^7 + 17^5 + 19^3 + 23^2.

Cf. A000040, A005408, A113122, A113153, A113154.

Sequence in context: A093904 A093344 A087316 this_sequence A104979 A081052 A020074

Adjacent sequences: A113168 A113169 A113170 this_sequence A113172 A113173 A113174

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 06 2006