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@MISC{June03kalmar'scomposition,
    author = {Steven Finch June and N Exp},
    title = {Kalmar's Composition Constant},
    year = {2003}
}

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Abstract:

ies [12] N # m p (n) # -1 #g , where # = -1.3994333287... is the unique solution of the equation g(y)= y =1,y<0. Not much is known about the number A p (n)ofprime additive partitions [13, 14, 15, 16] except that A p (n +1)>A p (n)forn # 8. Here is a related, somewhat artificial topic. Let p n be the n th prime, with p 1 =2, and define formal series P (z)=1+ # p n z ,Q(z)= P (z) = # q n z . Some people may be surprised to learn that the coe#cients q n obey the following asymptotics [17]: q n # #P 1 =(-0.6223065745...) (-1.4560749485...) . where # = -0.6867778344... is the unique zero of P (z) inside the disk |z| < 3/4. By way of contrast, p n # n ln(n) by the Prime Number Theorem. In a similar spirit, consider the coe#cients c k of the (n - 1) st degree polynomial fit c 0 + c 1 (x - 1) + c 2 (x - 1)(x - 2) + + c n-1 (x - 1)(x - 2)(x - 3) (x - n +1) to the dataset [18] (1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, 13), ...,(n, p n ). In the li

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