A121842 Difference between n^3 and next prime.

2, 1, 3, 2, 3, 2, 7, 4, 9, 4, 9, 30, 5, 6, 5, 14, 3, 6, 7, 4, 9, 16, 3, 30, 5, 4, 3, 4, 9, 2, 11, 12, 3, 14, 9, 24, 7, 18, 5, 14, 7, 6, 5, 24, 9, 2, 31, 14, 5, 10, 3, 10, 3, 14, 13, 18, 5, 28, 9, 12, 23, 10, 3, 2, 3, 2, 5, 16, 9, 2, 19, 2, 25, 6, 3, 16, 3, 6, 5, 4, 9, 16, 13, 2, 19, 4, 3, 4, 9, 14

Offset: 0

Author

Zak Seidov, Aug 29 2006

Keywords

• nonn
• easy

Comments

From Ingham (1937) it follows that there is a prime between x^3 and (x+1)^3 if x is sufficiently large: see A060199 for further details. - M. F. Hasler, Nov 09 2020

Examples

			a(6)=7 because next prime after 6^3=216 is 223 and 223-216=7.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
• A. E. Ingham, On the difference between consecutive primes. Quarterly Journal of Mathematics. Oxford Series. 8 (1) (1937) p. 255-266 (doi:10.1093/qmath/os-8.1.255).

Crossrefs

Cf. A060199 (number of primes between consecutive cubes).

Programs

Mathematica

Array[NextPrime[#] - # &[#^3] &, 90, 0] (* Michael De Vlieger, Nov 12 2020 *)

PARI

a(n) = nextprime(n^3) - n^3; \\ Michel Marcus, Oct 10 2013

Formula

a(n) = A013632(n^3) = A013632(A000578(n)). - Michel Marcus, Oct 10 2013