A073736 Sum of primes whose index is congruent to n (mod 3); equals the partial sums of A073737 (in which sums of three successive terms form the primes).

1, 2, 3, 6, 9, 14, 19, 26, 33, 42, 55, 64, 79, 96, 107, 126, 149, 166, 187, 216, 237, 260, 295, 320, 349, 392, 421, 452, 499, 530, 565, 626, 661, 702, 765, 810, 853, 922, 973, 1020, 1095, 1152, 1201, 1286, 1345, 1398, 1485, 1556, 1621, 1712, 1785, 1854, 1951

Offset: 0

Author

Paul D. Hanna, Aug 07 2002

Keywords

• easy
• nice
• nonn

Comments

For purposes of this sequence, 1 is treated as a prime. - Harvey P. Dale, Jul 24 2013

Examples

			a(10) = p_10 + p_7 + p_4 + p_1 = 29 + 17 + 7 + 2 = 55.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A073737.

Programs

Haskell

a073736 n = a073736_list !! n
a073736_list = scanl1 (+) a073737_list
-- Reinhard Zumkeller, Apr 28 2013

Mathematica

a[0] = 1; a[-1] = 0; a[-2] = 0; p[0] = 1; p[n_?Positive] := Prime[n]; a[n_] := a[n] = p[n] - a[n-1] - a[n-2]; Table[a[n], {n, 0, 60}] // Accumulate (* Jean-François Alcover, Jun 25 2013 *)
Sort[Flatten[Accumulate/@Transpose[Partition[Join[{1},Prime[Range[61]]], 3]]]] (* Harvey P. Dale, Jul 24 2013 *)

Formula

a(n) = Sum_{m<=n, m=n (mod 3)} p_m, where p_m is the m-th prime; that is, a(3n+k) = p_(3n) + p_(3(n-1)) + p_(3(n-2)) + ... + p_k, for 0<=k<3, where a(0)=1 and the 0th prime is taken to be 1.