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A133450 Difference between 4*n^2 and the average of the two prime numbers which bracket this number.

%I A133450 #15 Aug 31 2017 12:46:54
%S A133450 0,1,2,0,1,0,1,2,0,1,1,2,1,4,3,-2,-2,2,1,1,-4,-5,-5,1,10,1,3,7,-2,0,4,
%T A133450 0,3,-5,4,0,2,12,0,-9,-2,6,-6,-3,3,0,2,1,-3,10,-9,1,10,-3,1,0,4,2,-2,
%U A133450 5,1,1,8,-12,5,-1,8,-2,0,0,-3,-1,1,2,8,-4,12,3,4,5,1,-2,-10,0,10
%N A133450 Difference between 4*n^2 and the average of the two prime numbers which bracket this number.
%H A133450 G. C. Greubel, <a href="/A133450/b133450.txt">Table of n, a(n) for n = 1..1000</a>
%F A133450 a(n) = A056929(2n). - _M. F. Hasler_, Dec 26 2007
%e A133450 a(1)=0 because 4 - (3 + 5)/2 = 0
%e A133450 a(2)=1 because 16 - (13 + 17)/2 = 1
%e A133450 a(3)=2 because 36 - (31 + 37)/2 = 2
%e A133450 a(4)=0 because 64 - (61 + 67)/2 = 0
%e A133450 a(5)=1 because 100 - (97 + 101)/2 = 1
%t A133450 Table[n^2-(Prime[PrimePi[n^2]]+Prime[PrimePi[n^2]+1])/2,{n,2,200,2}] (* _Zak Seidov_ *)
%t A133450 diff4[n_]:=Module[{x=4n^2},x-(NextPrime[x]+NextPrime[x,-1])/2]; Array[ diff4,90] (* _Harvey P. Dale_, Aug 31 2017 *)
%o A133450 (PARI) A133450(n)=4*n^2-(precprime(4*n^2)+nextprime(4*n^2))/2 \\ _M. F. Hasler_, Dec 26 2007
%Y A133450 Cf. A056929, A101593, A075190.
%K A133450 sign
%O A133450 1,3
%A A133450 _Alexander R. Povolotsky_, Dec 22 2007
%E A133450 Corrected and extended by _Zak Seidov_, Dec 23 2007
%E A133450 Edited by _N. J. A. Sloane_, Dec 23 2007