A113173 Ascending descending base exponent transform of semiprimes (A001358).

256, 5392, 315361, 11667713, 717360537, 83932270482, 27775696582531, 22260761742531649, 109563850113131234720, 2013390472722146301196, 1899501614194512059559835, 85600281199526209989968735

Offset: 1

Author

Jonathan Vos Post, Jan 07 2006

Keywords

• easy
• nonn

Comments

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?

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..100

Crossrefs

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

Programs

Mathematica

A001358[A001358%5Bk%5D%5B%5Bk%5D%5D)%5E((A001358%5Bn%20-%20k%20+%201%5D%5B%5Bn%20-%20k%20+%201%5D%5D)),%20%7Bk,%201,%20n%7D%5D,%20%7Bn,%201,%2010%7D%5D%20(*%20_G.%20C.%20Greubel">] := Select[Range[100], PrimeOmega[#] == 2 &]; Table[Sum[(A001358[k][[k]])^((A001358[n - k + 1][[n - k + 1]])), {k, 1, n}], {n, 1, 10}] (* _G. C. Greubel, May 19 2017 *)

Formula

a(n) = Sum_{i=1..n} (semiprime(i))^(semiprime(n-i+1)).

a(n) = Sum_{i=1..n} (A001358(i))^(A001358(n-i+1)).