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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A047972.

Sequence in context: A198811 A067337 A180091 * A020501 A283878 A086404

Adjacent sequences: A047970 A047971 A047972 * A047974 A047975 A047976

Keyword

easy,nonn

Author

Enoch Haga

Status

approved