A182155 Integers of the form: 0/3 + 1/3 + 2/3 + 3/3 + 5/3 + 7/3 + 11/3 + 13/3 + 17/3 + ....

0, 1, 2, 6, 14, 26, 66, 94, 147, 264, 663, 759, 916, 1089, 1213, 1343, 1554, 1706, 2113, 2473, 2661, 2861, 3069, 3285, 3513, 3747, 3989, 4497, 4763, 5039, 5323, 5911, 6217, 6527, 6849, 7179, 7690, 8227, 8790, 9566, 9966, 10995, 11423, 12076, 12974, 13438

Offset: 1

Author

Gerasimov Sergey, Apr 15 2012

Keywords

• nonn

Comments

Numbers k such that the sum of first n nonnegative noncomposite numbers is equal to 3k.

Examples

			1/3 + 2/3 = 1, 1/3 + 2/3 + 3/3 = 2, 1/3 + 2/3 + 3/3 + 5/3 + 7/3 = 6.
		

Links

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

Crossrefs

Cf. A007504, A154293, A158611.

Programs

Mathematica

s = 1; t = {0}; Do[s = s + Prime[n]; If[Mod[s, 3] == 0, AppendTo[t, s/3]], {n, 200}]; t (* T. D. Noe, Apr 18 2012 *)
Select[Accumulate[Join[{0,1/3},Prime[Range[200]]/3]],IntegerQ] (* Harvey P. Dale, Mar 06 2016 *)

Extensions

Definition corrected by Harvey P. Dale, Mar 06 2016