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%I #19 Feb 21 2022 12:33:24
%S 11,33,70,139,238,372,552,775,1058,1410,1800,2290,2851,3501,4232,5067,
%T 6006,7048,8213,9496,10901,12450,14124,15951,17928,20059,22358,24822,
%U 27470,30284,33296,36504,39898,43514,47325,51364,55597,60105,64822
%N Difference between average of smallest prime greater than n^3 and largest prime less than (n+1)^3 and n-th pronic [=n(n+1)].
%C First term is not an integer.
%H Harry J. Smith, <a href="/A063036/b063036.txt">Table of n, a(n) for n = 2..1000</a>
%e n=4: a(4) = 70 because the smallest prime greater than 4^3 is 67, the largest prime less than 5^3 is 113, the average of 67 and 113 is 90, and 90 - 4*5 = 70.
%t Table[Mean[{NextPrime[n^3],NextPrime[(n+1)^3,-1]}]-n(n+1),{n,2,40}] (* _Harvey P. Dale_, Feb 21 2022 *)
%o (PARI) j=[]; for(n=2,60,j=concat(j,((precprime((n+1)^3)+nextprime(n^3))/2)- (n*(n+1))))); j
%o (PARI) { for (n=2, 1000, a=(precprime((n + 1)^3) + nextprime(n^3))/2 - n*(n + 1); write("b063036.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 16 2009
%K easy,nonn
%O 2,1
%A _Jason Earls_, Aug 03 2001
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