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 A121842 Difference between n^3 and next prime. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)