A075675 - OEIS

%I #11 Jun 30 2020 15:13:27

%S 4,18,74,182,358,746,1176,1854,2650,3870,5696,7358,9818,13052,16134,

%T 19742,24192,30048,36306,42932,50954,59904,70210,82646,93446,105640,

%U 117558,131950,148108,165772

%N Sum of next n even interprimes.

%C Sum of next n primes in A007468. Sum of next n integer interprimes in A075673. Sum of next n odd interprimes in A075674.

%H Harvey P. Dale, <a href="/A075675/b075675.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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}]

%t 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 *)

%Y Cf. A007468, A075673, A075674, A075675.

%K nonn

%O 1,1

%A _Zak Seidov_, Sep 24 2002