A063933 - OEIS

A063933

Difference between n and the average of largest prime less than or equal to n and smallest prime greater than or equal to n.

0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, -2, -1, 0, 1, 2, 0, 0, 0, -2, -1, 0, 1, 2, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, 0, 0, -2, -1, 0, 1, 2, 0, -1, 0, 1, 0, 0, 0, -2, -1, 0, 1, 2, 0, -1, 0, 1, 0, -2, -1, 0, 1, 2, 0, -3, -2, -1, 0, 1, 2, 3, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,23

LINKS

Harry J. Smith, Table of n, a(n) for n = 2..1000

FORMULA

a(n) = n - (A007917(n) + A007918(n))/2 = n - A063932(n).

a(n) = 0 for numbers in A063934 (i.e., in A000040 or A024675).

EXAMPLE

a(10) = 10 - (11 - 7)/2 = 1; a(11) = 11 - (11 + 11)/2 = 0.

PROG

(PARI) { for (n=2, 1000, write("b063933.txt", n, " ", n - (precprime(n) + nextprime(n))/2) ) } \\ Harry J. Smith, Sep 03 2009