A014220 Next prime after n^3.

2, 2, 11, 29, 67, 127, 223, 347, 521, 733, 1009, 1361, 1733, 2203, 2749, 3389, 4099, 4919, 5839, 6863, 8009, 9277, 10651, 12197, 13829, 15629, 17579, 19687, 21961, 24391, 27011, 29803, 32771, 35951, 39313

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

According to Borwein's Remark 1, this is an example of a sequence of primes whose mean value is in [0,1]. - T. D. Noe, Sep 15 2008

More precisely, Borwein, Choi and Coons remark that the generalized Liouville function for this sequence has mean value in (0,1). - Jonathan Sondow, May 19 2013

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000 (first 1000 terms from T. D. Noe)
• Peter Borwein, Stephen K.K. Choi and Michael Coons, Completely multiplicative functions taking values in {-1,1}, arXiv:0809.1691 [math.NT], 2008.

Crossrefs

Cf. A007491, A060199.

Programs

Mathematica

NextPrime[Range[0, 100]^3] (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)

PARI

a(n)=nextprime(n^3) \\ Charles R Greathouse IV, May 26 2015

Formula

a(n) < (n+1)^3 for n sufficiently large, by Ingham's theorem in A060199. - Jonathan Sondow, May 19 2013