|
%I #7 May 19 2017 02:37:13
%S 256,5392,315361,11667713,717360537,83932270482,27775696582531,
%T 22260761742531649,109563850113131234720,2013390472722146301196,
%U 1899501614194512059559835,85600281199526209989968735
%N Ascending descending base exponent transform of semiprimes (A001358).
%C 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?
%H G. C. Greubel, <a href="/A113173/b113173.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = Sum_{i=1..n} (semiprime(i))^(semiprime(n-i+1)).
%F a(n) = Sum_{i=1..n} (A001358(i))^(A001358(n-i+1)).
%e a(1) = 256 because semiprime(1)^semiprime(1) = 4^4 = 256.
%e a(2) = 5392 because prime(1)^prime(2) + prime(2)^prime(1) = 4^6 + 6^4 = 5392.
%e a(3) = 315361 because 4^9 + 6^6 + 9^4 = 315361.
%e a(4) = 11667713 = 4^10 + 6^9 + 9^6 + 10^4.
%e a(5) = 717360537 = 4^14 + 6^10 + 9^9 + 10^6 + 14^4.
%e a(6) = 83932270482 = 4^15 + 6^14 + 9^10 + 10^9 + 14^6 + 15^4.
%e a(7) = 27775696582531 = 4^21 + 6^15 + 9^14 + 10^10 + 14^9 + 15^6 + 21^4.
%e a(8) = 22260761742531649 = 4^22 + 6^21 + 9^15 + 10^14 + 14^10 + 15^9 + 21^6 + 22^4.
%e a(9) = 109563850113131234720 = 4^25 + 6^22 + 9^21 + 10^15 + 14^14 + 15^10 + 21^9 + 22^6 + 25^4.
%t A001358[_] := 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 *)
%Y Cf. A001358, A005408, A113122, A113153, A113154.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jan 07 2006
| 