A073738 Sum of every other prime <= n-th prime down to 2 or 1; equals the partial sums of A036467 (in which sums of two consecutive terms form the primes).

1, 2, 4, 7, 11, 18, 24, 35, 43, 58, 72, 89, 109, 130, 152, 177, 205, 236, 266, 303, 337, 376, 416, 459, 505, 556, 606, 659, 713, 768, 826, 895, 957, 1032, 1096, 1181, 1247, 1338, 1410, 1505, 1583, 1684, 1764, 1875, 1957, 2072, 2156, 2283, 2379, 2510, 2608

Offset: 0

Author

Paul D. Hanna, Aug 07 2002

Keywords

• easy
• nice
• nonn

Examples

			a(10) = p_10 + p_8 + p_6 + p_4 + p_2 + p_0 = 29 + 19 + 13 + 7 + 3 + 1 = 72.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Harvey P. Dale)

Crossrefs

Cf. A000040, A036467, A073736.

Cf. A006005.

Programs

Haskell

a073738 n = a073738_list !! n
a073738_list = tail zs where
   zs = 1 : 1 : zipWith (+) a006005_list zs
-- Reinhard Zumkeller, Apr 28 2013

Maple

a:= proc(n) a(n):= `if`(n<1, n+1, ithprime(n) + a(n-2)) end:
seq(a(n), n=0..50);  # Alois P. Heinz, Jun 04 2021

Mathematica

nn=60;Join[{1},Sort[Join[Accumulate[Prime[Range[1,nn+1,2]]], 1+#&/@ Accumulate[Prime[Range[2,nn,2]]]]]] (* Harvey P. Dale, May 04 2011 *)

Formula

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

a(n) = prime(n) + a(n-2) for n >= 2. - Alois P. Heinz, Jun 04 2021