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A102552
a(n) = prime(n)-(prime(n+1)+prime(n-1))/2.
3
0, -1, 1, -1, 1, -1, -1, 2, -2, 1, 1, -1, -1, 0, 2, -2, 1, 1, -2, 1, -1, -1, 2, 1, -1, 1, -1, -5, 5, -1, 2, -4, 4, -2, 0, 1, -1, 0, 2, -4, 4, -1, 1, -5, 0, 4, 1, -1, -1, 2, -4, 2, 0, 0, 2, -2, 1, 1, -4, -2, 5, 1, -1, -5, 4, -2, 4, -1, -1, -1, 1, 0, 1, -1, -1, 2, -2, -1, 4, -4, 4, -2, 1, -1, -1, 2, 1, -1, -4, 2, 2, -2, 2, -1, -3, 5, -8, 6, -2, 2, 0, 2, -2
OFFSET
3,8
REFERENCES
Eric Weisstein, CRC Concise Encyclopedia of Mathematics, 1998, page 1321.
FORMULA
a(n) = -(1/2)*(A001223(n+1)-A001223(n))
a(n) = -A036263(n-1)/2. - T. D. Noe, Oct 06 2006 [corrected by Georg Fischer, Oct 19 2023]
EXAMPLE
a(6)=-1 because 13-(17+11)/2=-1.
MAPLE
a:=n->ithprime(n)-(ithprime(n+1)+ithprime(n-1))/2: seq(a(n), n=3..95); # Emeric Deutsch, Mar 02 2005
MATHEMATICA
f[n_] := Prime[n] - (Prime[n - 1] + Prime[n + 1])/2; Table[f[n], {n, 3, 107}] (* Robert G. Wilson v, Sep 25 2006 *)
#[[2]]-(#[[1]]+#[[3]])/2&/@Partition[Prime[Range[2, 110]], 3, 1] (* Harvey P. Dale, Sep 21 2013 *)
PROG
(PARI) a(n) = prime(n)-(prime(n+1)+prime(n-1))/2;
vector(100, n, a(n+2)) \\ Joerg Arndt, Jan 20 2015
(Python)
from sympy import sieve as p
def A102552(n): return p[n]-(p[n+1]+p[n-1])//2 # Karl-Heinz Hofmann, May 22 2024
CROSSREFS
KEYWORD
sign
AUTHOR
Yasutoshi Kohmoto, Feb 25 2005
EXTENSIONS
More terms from Emeric Deutsch, Mar 02 2005
STATUS
approved