A Variation on Mills-Like Prime-Representing Functions
Rue des Tanneurs 7
Grand Duchy of Luxembourg
Mills showed that there exists a constant A such that
⌊ A3n ⌋ is prime for
every positive integer n. Kuipers and Ansari generalized
this result to
⌊ Acn ⌋
where c ∈ R and c ≥ 2.106.
The main contribution of this paper is a proof
that the function
⌈ Bcn ⌉
is also a prime-representing function, where
⌈ X ⌉
denotes the ceiling or least integer function. Moreover, the first 10
primes in the sequence generated in the case c = 3 are calculated.
Lastly, the value of
B is approximated to the first 5500 digits and is
shown to begin with 1.2405547052... .
Full version: pdf,
(Concerned with sequences
Received June 8 2017; revised versions received September 20 2017; September 26 2017.
Published in Journal of Integer Sequences, October 29 2017.
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