A094931 - OEIS

%I #12 Nov 15 2019 09:02:48

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

%C 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 := proc(n)

%p     local p3,p2,p1,p0 ;

%p     p3 := ithprime(n-3) ;

%p     p2 := ithprime(n-2) ;

%p     p1 := ithprime(n-1) ;

%p     p0 := ithprime(n) ;

%p     max(p3-3*p2+p1+p0,0) ;

%p end proc:

%p seq(A094931(n),n=4..50) ; # _R. J. Mathar_, Nov 15 2019

%t 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 If[#<=0,0,#]&/@(4(Total[#]/4-#[[2]])&/@Partition[Prime[Range[90]],4,1]) (* _Harvey P. Dale_, Mar 02 2015 *)

%Y Cf. A034963.

%K nonn,less

%O 4,1

%A _Roger L. Bagula_, Jun 17 2004