A104148 Difference between n^3 and largest m less than n^3, where m > 0 is either a prime or a square.

1, 2, 3, 4, 5, 6, 3, 2, 3, 4, 5, 18, 3, 2, 3, 4, 5, 2, 7, 4, 9, 4, 17, 6, 3, 2, 9, 10, 7, 2, 7, 4, 3, 12, 7, 2, 3, 38, 3, 4, 11, 14, 25, 4, 9, 10, 5, 6, 9, 4, 5, 4, 7, 12, 15, 4, 9, 22, 17, 38, 7, 4, 5, 16, 5, 2, 9, 28, 11, 28, 17, 14, 3, 28, 9, 4, 5, 12, 3, 58, 5

Offset

2,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Formula

a(n) < 2n^(3/2) - 1. Conjecturally a(n) << log^2 n. - Charles R Greathouse IV, Jun 03 2013

Example

a(5) = 4 because largest square less than 5^3 is 121 and 125 - 121 = 4.

Mathematica

lst = {}; Do[k = n^3; a = NextPrime[k, -1]; b = Floor@Sqrt[k - 1]^2; AppendTo[lst, k - Max[a, b]], {n, 2, 82}]; lst (* Arkadiusz Wesolowski, Jun 03 2013 *)

Prog

(Magma) [n^3-Maximum(Isqrt(n^3-1)^2, PreviousPrime(n^3)): n in [2..100]]; // Bruno Berselli, Jun 03 2013
(PARI) a(n)=n^3-max(sqrtint(n^3-1)^2, precprime(n^3)) \\ Charles R Greathouse IV, Jun 03 2013

Crossrefs

Sequence in context: A043266 A082120 A352425 * A286450 A382108 A245344

Adjacent sequences: A104145 A104146 A104147 * A104149 A104150 A104151

Keyword

nonn,easy

Author

Giovanni Teofilatto, Mar 08 2005

Extensions

Offset corrected by Michel Marcus, Jun 03 2013

Edited, corrected and extended by Arkadiusz Wesolowski, Jun 03 2013

Status

approved