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
a(1) = (7+11)/2 = 9; a(2) = (13+17)/2+(19+23)/2 = 15 + 21 = 36.
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(* 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}]
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
a(1) = (3+5)/2 = 4; a(2) = (5+7)/2+(11+13)/2 = 6 + 12 = 18.
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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 *)
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