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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A331317 A259664 A321880 * A062827 A074448 A297088

Adjacent sequences: A075670 A075671 A075672 * A075674 A075675 A075676

Keyword

nonn

Author

Zak Seidov, Sep 24 2002

Status

approved