A047973 Distance of n-th prime to nearest cube.

1, 2, 3, 1, 3, 5, 9, 8, 4, 2, 4, 10, 14, 16, 17, 11, 5, 3, 3, 7, 9, 15, 19, 25, 28, 24, 22, 18, 16, 12, 2, 6, 12, 14, 24, 26, 32, 38, 42, 43, 37, 35, 25, 23, 19, 17, 5, 7, 11, 13, 17, 23, 25, 35, 41, 47, 53, 55, 61, 62, 60, 50, 36, 32, 30, 26, 12, 6, 4, 6, 10, 16, 24, 30, 36, 40

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn

Examples

			For 179, 125 is the preceding cube, 216 is the succeeding. 179-125 = 54, 216-179 = 37, so the distance is 37.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A047972.

Programs

Mathematica

dnc[n_]:=Module[{c=Surd[n,3]},Min[Ceiling[c]^3-n,n-Floor[c]^3]]; dnc/@ Prime[Range[80]] (* Harvey P. Dale, Jan 11 2017 *)

PARI

a(n) = {p = prime(n); sc = sqrtnint(p, 3); min(p - sc^3, (sc+1)^3 - p);} \\ Michel Marcus, Jun 05 2014

Formula

For each prime, find the closest cube (preceding or succeeding); subtract, take absolute value.