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

%I A102552 #34 Feb 02 2025 15:35:31
%S A102552 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,
%T A102552 -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,
%U A102552 -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
%N A102552 a(n) = prime(n) - (prime(n+1) + prime(n-1))/2.
%D A102552 Eric Weisstein, CRC Concise Encyclopedia of Mathematics, 1998, page 1321.
%H A102552 G. C. Greubel, <a href="/A102552/b102552.txt">Table of n, a(n) for n = 3..10000</a>
%F A102552 a(n) = (1/2)*(A001223(n) - A001223(n+1)).
%F A102552 a(n) = -A036263(n-1)/2. - _T. D. Noe_, Oct 06 2006 [corrected by _Georg Fischer_, Oct 19 2023]
%e A102552 a(6)=-1 because 13-(17+11)/2=-1.
%p A102552 a:=n->ithprime(n)-(ithprime(n+1)+ithprime(n-1))/2: seq(a(n),n=3..95); # _Emeric Deutsch_, Mar 02 2005
%t A102552 f[n_] := Prime[n] - (Prime[n - 1] + Prime[n + 1])/2; Table[f[n], {n, 3, 107}] (* _Robert G. Wilson v_, Sep 25 2006 *)
%t A102552 #[[2]]-(#[[1]]+#[[3]])/2&/@Partition[Prime[Range[2,110]],3,1] (* _Harvey P. Dale_, Sep 21 2013 *)
%o A102552 (PARI) a(n) = prime(n)-(prime(n+1)+prime(n-1))/2;
%o A102552 vector(100,n,a(n+2)) \\ _Joerg Arndt_, Jan 20 2015
%o A102552 (Python)
%o A102552 from sympy import sieve as p
%o A102552 def A102552(n): return p[n]-(p[n+1]+p[n-1])//2 # _Karl-Heinz Hofmann_, May 22 2024
%o A102552 (Magma)
%o A102552 A102552:= func< n | (2*NthPrime(n)-NthPrime(n+1)-NthPrime(n-1))/2 >;
%o A102552 [A102552(n): n in [3..120]]; // _G. C. Greubel_, Feb 02 2025
%Y A102552 Cf. A000040, A006562, A036263, A051634, A051635, A066875.
%K A102552 sign
%O A102552 3,8
%A A102552 _Yasutoshi Kohmoto_, Feb 25 2005
%E A102552 More terms from _Emeric Deutsch_, Mar 02 2005