A073738 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

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

EXAMPLE

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

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 *)

PROG

(Haskell)

a073738 n = a073738_list !! n

a073738_list = tail zs where