0,1

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

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).

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

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

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

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

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

Sequence in context: A100677 A188637 A083290 * A317963 A219609 A087825

Adjacent sequences: A121839 A121840 A121841 * A121843 A121844 A121845

nonn,easy

Zak Seidov, Aug 29 2006

approved