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A047973 Distance of n-th prime to nearest cube. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 24 00:19 EST 2020. Contains 332195 sequences. (Running on oeis4.)