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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).

%I A073738 #19 Jun 04 2021 10:43:07
%S A073738 1,2,4,7,11,18,24,35,43,58,72,89,109,130,152,177,205,236,266,303,337,
%T A073738 376,416,459,505,556,606,659,713,768,826,895,957,1032,1096,1181,1247,
%U A073738 1338,1410,1505,1583,1684,1764,1875,1957,2072,2156,2283,2379,2510,2608
%N 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).
%H A073738 Alois P. Heinz, <a href="/A073738/b073738.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from Harvey P. Dale)
%F A073738 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.
%F A073738 a(n) = prime(n) + a(n-2) for n >= 2. - _Alois P. Heinz_, Jun 04 2021
%e A073738 a(10) = p_10 + p_8 + p_6 + p_4 + p_2 + p_0 = 29 + 19 + 13 + 7 + 3 + 1 = 72.
%p A073738 a:= proc(n) a(n):= `if`(n<1, n+1, ithprime(n) + a(n-2)) end:
%p A073738 seq(a(n), n=0..50);  # _Alois P. Heinz_, Jun 04 2021
%t A073738 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 *)
%o A073738 (Haskell)
%o A073738 a073738 n = a073738_list !! n
%o A073738 a073738_list = tail zs where
%o A073738    zs = 1 : 1 : zipWith (+) a006005_list zs
%o A073738 -- _Reinhard Zumkeller_, Apr 28 2013
%Y A073738 Cf. A000040, A036467, A073736.
%Y A073738 Cf. A006005.
%K A073738 easy,nice,nonn
%O A073738 0,2
%A A073738 _Paul D. Hanna_, Aug 07 2002