A072475 Sum of next n composite numbers.

4, 14, 31, 63, 112, 176, 264, 385, 529, 712, 932, 1184, 1503, 1833, 2234, 2689, 3207, 3779, 4408, 5117, 5913, 6747, 7657, 8667, 9766, 10938, 12240, 13612, 15071, 16578, 18266, 20081, 22007, 23989, 26100, 28334, 30695, 33221, 35811, 38569, 41474

Offset: 1

Author

Amarnath Murthy, Jun 20 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A072474, A007468, A006003.

Programs

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Table[ Sum[ Composite[i], {i, n(n - 1)/2 + 1, n(n + 1)/2}], {n, 1, 42}]
With[{terms=50},cnos=With[{c=(terms(terms+1)(terms+2))/6}, Complement[ Range[5,c], Prime[Range[PrimePi[c]]]]];Join[{4}, Total/@Table[Take[ cnos,{n (n+1)/2,(n+1) (n+2)/2-1}],{n,terms-1}]]] (* Harvey P. Dale, Oct 10 2011 *)

Extensions

More terms from Jim Nastos and Robert G. Wilson v, Jun 21 2002