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A075673
Sum of next n integer interprimes (cf. A024675).
3
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
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 24 2002
STATUS
approved