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

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

Offset

1,1

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?

Links

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

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)).

Example

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.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A200790 A206110 A196152 * A223964 A195595 A204567

Adjacent sequences: A113170 A113171 A113172 * A113174 A113175 A113176

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 07 2006

Status

approved