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A056931 Difference between n-th pronic [=n(n+1)] and average of smallest prime greater than n^2 and largest prime less than (n+1)^2. 5

%I

%S 0,0,0,0,0,-1,-1,0,3,-1,-2,-1,0,1,2,1,-3,-2,0,1,1,-4,2,-2,0,3,-1,0,0,

%T -2,-3,0,-3,0,0,0,3,0,5,-4,-6,-5,-3,0,-6,1,-2,6,2,-2,1,-2,0,1,9,0,2,

%U -2,-3,2,-1,-9,1,1,2,-1,-6,-6,-1,-3,0,0,0,6,-1,-3,3,-2,-7,1,-2,1,2,-1,-4

%N Difference between n-th pronic [=n(n+1)] and average of smallest prime greater than n^2 and largest prime less than (n+1)^2.

%C a(1)=-0.5 which is not an integer

%F a(n) =A002378(n)-(A007491(n)+A053001(n+1))/2 =A002378(n)-A056930(n).

%e a(4)=0 because smallest prime greater than 4^2 is 17, largest prime less than 5^2 is 23, average of 17 and 23 is 20 and 4*5-20=0

%p with(numtheory): A056931 := n-> n*(n+1)-(prevprime((n+1)^2)+nextprime(n^2))/2);

%Y Cf. A002378, A007491, A053000, A053001, A056927, A056928, A056929, A056930.

%K easy,sign

%O 2,9

%A _Henry Bottomley_, Jul 12 2000

%E More terms from _James A. Sellers_, Jul 13 2000

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)