Search: id:A113475
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%I A113475
%S A113475 1,3,5,2,4,2,2,4,2,4,3,2,5,3,3
%N A113475 Least integers so ascending descending base exponent transforms all semiprime.
%C A113475 Semiprime analogy to A113320. The sequence is probably infinite, but 
               it is hard to characterize the asymptotic cost of adding an n-th 
               term. The ascending descending base exponent transform of semiprimes 
               is A113173.
%F A113475 a(1) = 1. For n>1: a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(n-i+1)) 
               is semiprime}. a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(n-i+1)) 
               in A001358}.
%e A113475 a(1) = 1 by definition.
%e A113475 a(2) = 3 because 3 is the min x such that 1^x + x^1 is semiprime,
%e A113475 i.e. 1^3 + 3^1 = 4 = 2*2.
%e A113475 a(3) = 5 because 1^5 + 3^3 + 5^1 = 33 = 3 * 11 is semiprime.
%e A113475 a(4) = 2 because 1^2 + 3^5 + 5^3 + 2^1 = 371 = 7 * 53.
%e A113475 a(5) = 4 because 1^4 + 3^2 + 5^5 + 2^3 + 4^1 = 3147 = 3 * 1049.
%e A113475 a(6) = 2 because 1^2 + 3^4 + 5^2 + 2^5 + 4^3 + 2^1 = 205 = 5 * 41.
%e A113475 a(7) = 2 because 1^2 + 3^2 + 5^4 + 2^2 + 4^5 + 2^3 + 2^1 = 1673 = 7 * 
               239.
%e A113475 a(8) = 4 because 1^4 + 3^2 + 5^2 + 2^4 + 4^2 + 2^5 + 2^3 + 4^1 = 111 
               = 3 * 37.
%Y A113475 Cf. A001358, A005408, A113122, A113153, A113154, A113336, A113320, A113271, 
               A113258, A113257, A113231, A087316, A113208.
%Y A113475 Sequence in context: A091276 A076562 A156060 this_sequence A104807 A131793 
               A065186
%Y A113475 Adjacent sequences: A113472 A113473 A113474 this_sequence A113476 A113477 
               A113478
%K A113475 easy,nonn
%O A113475 1,2
%A A113475 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 08 2006

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