Search: id:A113122
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%I A113122
%S A113122 1,2,4,7,14,32,107,724,18616,4117597,28878084584,53183366452504936,
%T A113122 794001316484619940422835765,
%U A113122 25210343943654420841949267608211227900299990
%N A113122 Sum of the first n Fibonacci numbers, in ascending order, as bases, with 
               the same, in descending order, as exponents.
%C A113122 Primes begin a(2) = 2, a(4) = 7, a(7) = 107; what is the next prime? 
               This transform can be reflexively applied to any integer sequence 
               which does not give an indeterminate 0^0 term.
%F A113122 a(n) = SUM[from i = 1 to n] (F(i))^F(n-i+1)
%e A113122 a(1) = F(1)^F(1) = 1^1 = 1.
%e A113122 a(2) = F(1)^F(2) + F(2)^F(1) = 1^1 + 1^1 = 2.
%e A113122 a(3) = F(1)^F(3) + F(2)^F(2) + F(3)^F(1) = 1^2 + 1^1 + 2^1 = 4.
%e A113122 a(4) = F(1)^F(4) + F(2)^F(3) + F(3)^F(2) + F(4)^F(1) = 1^3 + 1^2 + 2^1 
               + 3^1 = 7.
%e A113122 a(5) = 1^5 + 1^3 + 2^2 + 3^1 + 5^1 = 14.
%e A113122 a(6) = 1^8 + 1^5 + 2^3 + 3^2 + 5^1 + 8^1 = 32.
%e A113122 a(7) = 1^13 + 1^8 + 2^5 + 3^3 + 5^2 + 8^1 + 13^1 = 107.
%e A113122 a(8) = 1^21 + 1^13 + 2^8 + 3^5 + 5^3 + 8^2 + 13^1 + 21^1 = 724.
%e A113122 a(9) = 1^34 + 1^21 + 2^13 + 3^8 + 5^5 + 8^3 + 13^2 + 21^1 + 34^1 = 18616.
%e A113122 a(10) = 1^55 + 1^34 + 2^21 + 3^13 + 5^8 + 8^5 + 13^3 + 21^2 + 34^1 + 
               55^1 = 4117597.
%e A113122 a(11) = 1^89 + 1^55 + 2^34 + 3^21 + 5^13 + 8^8 + 13^5 + 21^3 + 34^2 + 
               55^1 + 89^1 = 28878084584.
%e A113122 a(12) = 1^144 + 1^89 + 2^55 + 3^34 + 5^21 + 8^13 + 13^8 + 21^5 + 34^3 
               + 55^2 + 89^1 + 144^1 = 53183366452504936.
%e A113122 a(13) = 1^233 + 1^144 + 2^89 + 3^55 + 5^34 + 8^21 + 13^13 + 21^8 + 34^5 
               + 55^3 + 89^2 + 144^1 + 233^1 = 794001316484619940422835765.
%e A113122 a(14) = 1^377 + 1^233 + 2^144 + 3^89 + 5^55 + 8^34 + 13^21 + 21^13 + 
               34^8 + 55^5 + 89^3 + 144^2 + 233^1 + 377^1 = 25210343943654420841949267608211227900299990.
%Y A113122 Cf. A000045.
%Y A113122 Sequence in context: A120262 A013326 A074663 this_sequence A116584 A152477 
               A019998
%Y A113122 Adjacent sequences: A113119 A113120 A113121 this_sequence A113123 A113124 
               A113125
%K A113122 easy,nonn
%O A113122 1,2
%A A113122 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 04 2006

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