A102552 a(n) = prime(n) - (prime(n+1) + prime(n-1))/2.

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

Author

Yasutoshi Kohmoto, Feb 25 2005

Keywords

• sign

Examples

			a(6)=-1 because 13-(17+11)/2=-1.
		

References

• Eric Weisstein, CRC Concise Encyclopedia of Mathematics, 1998, page 1321.

Links

• G. C. Greubel, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000040, A006562, A036263, A051634, A051635, A066875.

Programs

Magma

A102552:= func< n | (2*NthPrime(n)-NthPrime(n+1)-NthPrime(n-1))/2 >;
[A102552(n): n in [3..120]]; // G. C. Greubel, Feb 02 2025

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 *)

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

Formula

a(n) = (1/2)*(A001223(n) - A001223(n+1)).

a(n) = -A036263(n-1)/2. - T. D. Noe, Oct 06 2006 [corrected by Georg Fischer, Oct 19 2023]

Extensions

More terms from Emeric Deutsch, Mar 02 2005