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A094931 A measure of the excess of the mean of the set of 4 consecutive primes over the 2nd of the set.

%I A094931 #12 Nov 15 2019 09:02:48
%S A094931 5,6,8,4,8,4,12,10,4,14,4,4,12,14,8,4,14,4,6,14,8,16,14,2,4,8,4,20,28,
%T A094931 0,10,8,20,0,16,10,8,14,8,8,20,0,8,12,34,16,0,4,12,10,8,24,8,12,8,4,
%U A094931 14,4,10,32,22,0,4,20,30,8,16,0,12,16,16,10,10,8,16,14,8,22,14,4,20,0,14,8
%N A094931 A measure of the excess of the mean of the set of 4 consecutive primes over the 2nd of the set.
%C A094931 Let (prime(n-3)+prime(n-2)+prime(n-1)+prime(n))/4 = A034963(n-3)/4 be the arithmetic mean of 4 consecutive primes, and prime(n-2) the third largest. Then A034963(n-3)-4*prime(n-2) is an integer measure of the excess of the mean. We define a(n) by the excess if positive, else by 0.
%p A094931 A094931 := proc(n)
%p A094931     local p3,p2,p1,p0 ;
%p A094931     p3 := ithprime(n-3) ;
%p A094931     p2 := ithprime(n-2) ;
%p A094931     p1 := ithprime(n-1) ;
%p A094931     p0 := ithprime(n) ;
%p A094931     max(p3-3*p2+p1+p0,0) ;
%p A094931 end proc:
%p A094931 seq(A094931(n),n=4..50) ; # _R. J. Mathar_, Nov 15 2019
%t A094931 a=Table[If[(Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/4-Prime[n-2]>0, 4*((Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/4-Prime[n-2]), 0], {n, 4, 204}]
%t A094931 If[#<=0,0,#]&/@(4(Total[#]/4-#[[2]])&/@Partition[Prime[Range[90]],4,1]) (* _Harvey P. Dale_, Mar 02 2015 *)
%Y A094931 Cf. A034963.
%K A094931 nonn,less
%O A094931 4,1
%A A094931 _Roger L. Bagula_, Jun 17 2004