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A007918
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Least prime >= n (version 1 of the "next prime" function).
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106
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2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, 19, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 59, 59, 59, 59, 61, 61, 67, 67, 67, 67, 67, 67, 71, 71, 71, 71, 73, 73
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OFFSET
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0,1
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COMMENTS
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Version 2 of the "next prime" function is "smallest prime > n". This produces A151800.
Maple uses version 2.
According to the "k-tuple" conjecture, a(n) is the initial term of the lexicographically earliest increasing arithmetic progression of n primes; the corresponding common differences are given by A061558. - David W. Wilson, Sep 22 2007
It is easy to show that the initial term of an increasing arithmetic progression of n primes cannot be smaller than a(n). - N. J. A. Sloane, Oct 18 2007
Also, smallest prime bounded by n and 2n inclusively (in accordance with Bertrand's theorem). Smallest prime >n is a(n+1) and is equivalent to smallest prime between n and 2n exclusively. - Lekraj Beedassy, Jan 01 2007
Conjecture: if n > 1, then a(n) < n^(n^(1/n)). - Thomas Ordowski, Feb 23 2023
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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PROG
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(PARI) for(x=0, 100, print1(nextprime(x)", ")) \\ Cino Hilliard, Jan 15 2007
(Haskell)
a007918 n = a007918_list !! n
a007918_list = 2 : 2 : 2 : concat (zipWith
(\p q -> (replicate (fromInteger(q - p)) q))
a000040_list $ tail a000040_list)
(Python)
from sympy import nextprime
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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R. Muller and Charles T. Le (charlestle(AT)yahoo.com)
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STATUS
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approved
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