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

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, 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, 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

Offset: 4

Author

Roger L. Bagula, Jun 17 2004

Keywords

• nonn
• less

Comments

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.

Crossrefs

Cf. A034963.

Programs

Maple

A094931 := proc(n)
    local p3,p2,p1,p0 ;
    p3 := ithprime(n-3) ;
    p2 := ithprime(n-2) ;
    p1 := ithprime(n-1) ;
    p0 := ithprime(n) ;
    max(p3-3*p2+p1+p0,0) ;
end proc:
seq(A094931(n),n=4..50) ; # R. J. Mathar, Nov 15 2019

Mathematica

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