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 A113122 Sum of the first n Fibonacci numbers, in ascending order, as bases, with the same, in descending order, as exponents. 18
 1, 2, 4, 7, 14, 32, 107, 724, 18616, 4117597, 28878084584, 53183366452504936, 794001316484619940422835765, 25210343943654420841949267608211227900299990, 14311021641196256564899251685012421154803682074917148917844556724305980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS FORMULA a(n) = Sum_{i=1..n} F(i)^F(n-i+1). EXAMPLE a(1) = F(1)^F(1) = 1^1 = 1. a(2) = F(1)^F(2) + F(2)^F(1) = 1^1 + 1^1 = 2. a(3) = F(1)^F(3) + F(2)^F(2) + F(3)^F(1) = 1^2 + 1^1 + 2^1 = 4. 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. a(5) = 1^5 + 1^3 + 2^2 + 3^1 + 5^1 = 14. a(6) = 1^8 + 1^5 + 2^3 + 3^2 + 5^1 + 8^1 = 32. a(7) = 1^13 + 1^8 + 2^5 + 3^3 + 5^2 + 8^1 + 13^1 = 107. a(8) = 1^21 + 1^13 + 2^8 + 3^5 + 5^3 + 8^2 + 13^1 + 21^1 = 724. a(9) = 1^34 + 1^21 + 2^13 + 3^8 + 5^5 + 8^3 + 13^2 + 21^1 + 34^1 = 18616. a(10) = 1^55 + 1^34 + 2^21 + 3^13 + 5^8 + 8^5 + 13^3 + 21^2 + 34^1 + 55^1 = 4117597. 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. 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. 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. 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. MAPLE F:= n-> (<<0|1>, <1|1>>^n)[1, 2]: a:= n-> add(F(i)^F(n-i+1), i=1..n): seq(a(n), n=1..16);  # Alois P. Heinz, Aug 09 2018 MATHEMATICA Table[Sum[(Fibonacci[k])^((Fibonacci[n - k + 1]), {k, 1, n}], {n, 1, 10}] (* G. C. Greubel, May 18 2017 *) PROG (PARI) for(n=1, 10, print1(sum(k=1, n, (fibonacci(k))^(fibonacci(n-k+1))), ", ")) \\ G. C. Greubel, May 18 2017 CROSSREFS Cf. A000045. Sequence in context: A202973 A074663 A325303 * A296984 A116584 A152477 Adjacent sequences:  A113119 A113120 A113121 * A113123 A113124 A113125 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jan 04 2006 STATUS approved

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Last modified October 14 07:31 EDT 2019. Contains 327995 sequences. (Running on oeis4.)