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

0,2

Comments

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

Links

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

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A073737.

Sequence in context: A074150 A261243 A061925 * A101593 A349502 A226893

Adjacent sequences: A073733 A073734 A073735 * A073737 A073738 A073739

Keyword

easy,nice,nonn

Author

Paul D. Hanna, Aug 07 2002

Status

approved