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

4,1

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.

Links

Table of n, a(n) for n=4..87.

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 *)

Crossrefs

Cf. A034963.

Sequence in context: A091659 A271571 A349577 * A239354 A011498 A330863

Adjacent sequences: A094928 A094929 A094930 * A094932 A094933 A094934

Keyword

nonn,less

Author

Roger L. Bagula, Jun 17 2004

Status

approved