A075673 Sum of next n integer interprimes (cf. A024675).

4, 15, 45, 111, 232, 422, 704, 1129, 1667, 2403, 3287, 4470, 5810, 7508, 9414, 11663, 14363, 17454, 20715, 24739, 29214, 33957, 39183, 45540, 52056, 59497, 67181, 75862, 84831, 95697, 106608, 117812, 130356, 143759, 158617, 174312, 190500

Offset: 1

Author

Zak Seidov, Sep 24 2002

Keywords

• nonn

Comments

Sum of next n primes is A007468. Sum of next n odd interprimes is A075674. Sum of next n even interprimes is A075675.

Examples

			a(1) = (3+5)/2 = 4; a(2) = (5+7)/2+(7+11)/2 = 15; a(3) = (11+13)/2+(13+17)/2 +(17+19)/2 = 45.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A024675, A007468, A075673, A075674, A075675.

Programs

Mathematica

(* sum of next n integer interprimes*) i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; Table[Sum[(Prime[i+2]+Prime[i+1])/2, {i, i1, i2}], {n, 1, 40}]
With[{nn=40},Total/@TakeList[Mean/@Partition[Prime[Range[2,(nn(nn+1))/2+2]],2,1],Range[nn]]] (* Harvey P. Dale, Feb 24 2023 *)