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%I #17 Mar 13 2020 06:15:53
%S 0,1,2,-4,0,-1,-20,0,7,-10,-8,-2,-5,12,23,-28,-21,-8,-20,-15,-32,53,
%T -30,-47,10,-29,-48,33,-6,8,20,71,-5,-15,-6,3,109,23,-50,41,57,172,
%U -170,1,-122,-237,161,-8,91,-112,67,253,38,75,343,-188,43,88,123,96
%N a(n) = n^n - (PrevPrime(n^n) + NextPrime(n^n)) / 2.
%H Hugo Pfoertner, <a href="/A333184/b333184.txt">Table of n, a(n) for n = 2..1000</a>
%e n Previous P n^n Next P a(n)
%e A098681(n) A000312(n) A098682(n)
%e 2 3 4 5 0
%e 3 23 27 29 1
%e 4 251 256 257 2
%e 5 3121 3125 3137 -4
%e 6 46649 46656 46663 0
%e 7 823541 823543 823547 -1
%e 8 16777213 16777216 16777259 -20
%e 9 387420479 387420489 387420499 0
%e 10 9999999967 10000000000 10000000019 7
%p a:= n-> (m-> m-(prevprime(m)+nextprime(m))/2)(n^n):
%p seq(a(n), n=2..65); # _Alois P. Heinz_, Mar 10 2020
%o (PARI) for(n=2,61, my(f=n^n); print1(f-(precprime(f)+nextprime(f))/2,", "))
%Y Cf. A000312, A074966, A074967, A098681, A098682, A161503.
%Y Cf. A333185 (position of terms = 0).
%K sign
%O 2,3
%A _Hugo Pfoertner_, Mar 10 2020
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