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%I #21 Dec 14 2022 10:15:45
%S 0,0,1,-1,2,-1,0,0,1,1,0,-1,1,0,2,1,0,-2,1,0,1,-3,2,0,1,-1,4,-5,3,1,
%T -2,0,-2,-1,2,-1,1,4,1,0,-4,-5,-5,3,-5,-1,1,-4,10,0,1,-2,3,-5,7,9,-2,
%U 1,0,-2,4,-9,0,1,3,1,-5,-10,4,-4,0,1,2,-6,12,-4,0,3,-9,3,-2,-2,6,1,-6,2,-3
%N Difference between n^2 and average of smallest prime greater than n^2 and largest prime less than n^2.
%C Conjecture: the most frequent value will be 1 (including sequence variants with any even power n^2k). - _Bill McEachen_, Dec 12 2022
%H Hugo Pfoertner, <a href="/A056929/b056929.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = A000290(n) - A056928(n).
%F a(n) = (A056927(n) - A053000(n))/2.
%e a(4)=1 because smallest prime greater than 4^2 is 17, largest prime less than 4^2 is 13, average of 17 and 13 is 15 and 16-15=1.
%p with(numtheory): A056929 := n-> n^2-(prevprime(n^2)+nextprime(n^2))/2);
%t Array[# - Mean@ {NextPrime[#], NextPrime[#, -1]} &[#^2] &, 87, 2] (* _Michael De Vlieger_, May 20 2018 *)
%o (PARI) a(n) = n^2 - (nextprime(n^2) + precprime(n^2))/2; \\ _Michel Marcus_, May 20 2018
%Y Cf. A007491, A053000, A053001, A056927, A056928, A056930, A056931.
%K easy,sign
%O 2,5
%A _Henry Bottomley_, Jul 12 2000
%E More terms from _James A. Sellers_, Jul 13 2000
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