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 A113320 a(1)=1 and a(n) for n>1 has the smallest positive value such that Sum_{i=1..n} a(i)^a(n-i+1) is prime. 8
 1, 1, 1, 2, 2, 4, 4, 4, 6, 2, 6, 4, 18, 6, 4, 20, 6, 30, 4, 40, 30, 8, 18, 16, 40, 128, 24, 40, 58, 194, 78, 84, 56, 56, 72, 112, 98, 300, 444, 54, 978, 1938, 120, 126, 6, 1750 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Previous name was: Least integers so ascending descending base exponent transforms all prime. This is the first sequence submitted as a solution to an "ascending descending base exponent transform inverse problem" where the sequence is iteratively defined such that the transform meets a constraint. The sequence is infinite, but it is hard to characterize the asymptotic cost of adding an n-th term. 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. LINKS Table of n, a(n) for n=1..46. FORMULA a(1) = 1. For n>1, a(n) = min {k>0: a(1)^k + k^a(1) + Sum_{i=2..n-1} a(i)^a(n-i+1) is prime}. EXAMPLE a(1) = 1 by definition. a(2) = 1 because 1 is the min such that 1^a(2) + a(2)^1 is prime (p=2). a(3) = 1 because 1 is the min such that 1^a(3) + 1^1 + a(3)^1 is prime (p=5). a(4) = 2 because 2 is the min such that 1^a(4) + 1^1 + 3^1 + a(4)^1 is prime (p=7). MATHEMATICA inve[w_] := Total[w^Reverse[w]]; a[1] = 1; a[n_] := a[n] = Block[{k = 0}, While[! PrimeQ[ inve@ Append[Array[a, n-1], ++k]]]; k]; Array[a, 46] (* Giovanni Resta, Jun 13 2016 *) PROG (PARI) lista(n)={my(a=vector(n)); a[1]=1; print1(1, ", "); for(n=2, #a, my(t=sum(i=2, n-1, a[i]^a[n-i+1])); my(k=1); while(!ispseudoprime(t+1+k), k++); a[n]=k; print1(k, ", "))} \\ Andrew Howroyd, Jan 03 2020 CROSSREFS Cf. A000040, A005408, A113122, A113153, A113154. Sequence in context: A157887 A292264 A265263 * A085237 A279891 A110870 Adjacent sequences: A113317 A113318 A113319 * A113321 A113322 A113323 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jan 07 2006 EXTENSIONS Corrected and extended by Giovanni Resta, Jun 13 2016 New name from Giovanni Resta, Jan 03 2020 STATUS approved

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Last modified September 16 18:24 EDT 2024. Contains 375977 sequences. (Running on oeis4.)