A075675 -id:A075675 - cp's OEIS frontend

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

Zak Seidov, Sep 24 2002

nonn

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

			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.

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

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

(* 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 *)

A075674 Sum of next n odd interprimes.

Original entry on oeis.org

9, 36, 153, 378, 805, 1576, 2733, 3818, 5857, 8006, 10537, 14812, 19389, 23472, 29757, 36416, 44067, 52274, 61307, 71740, 86195, 104056, 120463, 138128, 158209, 181160, 205973, 229728, 255013, 281608

Offset: 1

Zak Seidov, Sep 24 2002

nonn

Sum of next n primes in A007468. Sum of next n integer interprimes in A075673. Sum of next n even interprimes in A075675.

			a(1) = (7+11)/2 = 9; a(2) = (13+17)/2+(19+23)/2 = 15 + 21 = 36.

Cf. A007468, A075673, A075674, A075675.

(* sum of next n odd interprimes*) od=Select[Table[(Prime[i]+Prime[i+1])/2, {i, 2, 2000}], OddQ]; i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; A075674=Table[Sum[od[[i]], {i, i1, i2}], {n, 30}]

cp's OEIS Frontend

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

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