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

0,1

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

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).

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Keyword

nonn,easy

Author

Zak Seidov, Aug 29 2006

Status

approved