A075674 -id:A075674 - 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 *)

A075675 Sum of next n even interprimes.

Original entry on oeis.org

4, 18, 74, 182, 358, 746, 1176, 1854, 2650, 3870, 5696, 7358, 9818, 13052, 16134, 19742, 24192, 30048, 36306, 42932, 50954, 59904, 70210, 82646, 93446, 105640, 117558, 131950, 148108, 165772

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 odd interprimes in A075674.

			a(1) = (3+5)/2 = 4; a(2) = (5+7)/2+(11+13)/2 = 6 + 12 = 18.

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

Cf. A007468, A075673, A075674, A075675.

ev=Select[Table[(Prime[i]+Prime[i+1])/2, {i, 2, 2000}], EvenQ]; (* sum of next n even interprimes*) i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; A075675=Table[Sum[ev[[i]], {i, i1, i2}], {n, 30}]
Module[{nn=1000,ip,len},ip=Select[Mean/@Partition[Prime[Range[nn]],2,1],EvenQ];len=Length[ip];Total/@TakeList[ip,Range[(Sqrt[1+8*len]-1)/2]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jun 30 2020 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica