Journal of Integer Sequences, Vol. 20 (2017), Article 17.9.8

A Variation on Mills-Like Prime-Representing Functions

László Tóth
Rue des Tanneurs 7
L-6790 Grevenmacher
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 cR 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... .

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(Concerned with sequences A051021 A051254.)

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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