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A333176 a(n) = Sum_{k=1..n} (binomial(n,k) mod 2) * prime(k).

%I A333176 #18 Jul 22 2025 14:02:59
%S A333176 2,3,10,7,20,23,58,19,44,51,112,63,140,151,328,53,114,117,250,131,276,
%T A333176 287,604,161,342,355,742,383,798,825,1720,131,270,273,566,289,596,607,
%U A333176 1252,323,664,675,1392,711,1458,1481,3046,407,832,839,1718,875,1782
%N A333176 a(n) = Sum_{k=1..n} (binomial(n,k) mod 2) * prime(k).
%H A333176 Robert Israel, <a href="/A333176/b333176.txt">Table of n, a(n) for n = 1..10000</a>
%F A333176 Sum_{k=1..n} (-1)^A010060(n-k) * (binomial(n,k) mod 2) * a(k) = prime(n).
%p A333176 N:= 200: # for a(1) .. a(N)
%p A333176 P:= [seq(ithprime(i),i=1..N)]:
%p A333176 B:= [1,1]: R:= 2:
%p A333176 for n from 2 to N do
%p A333176   B:= [1,op(B[2..-1]+B[1..-2] mod 2),1];
%p A333176   R:= R, convert(P[select(t -> B[t+1] = 1,[$1..n])],`+`);
%p A333176 od:
%p A333176 R; # _Robert Israel_, Jan 29 2025
%t A333176 Table[Sum[Mod[Binomial[n, k], 2] Prime[k], {k, 1, n}], {n, 1, 53}]
%o A333176 (PARI) a(n) = sum(k=1, n, if (binomial(n, k) % 2, prime(k))); \\ _Michel Marcus_, Mar 10 2020
%o A333176 (Python)
%o A333176 from sympy import prime
%o A333176 def A333176(n): return sum(prime(k) for k in range(1,n+1) if not ~n&k) # _Chai Wah Wu_, Jul 22 2025
%Y A333176 Cf. A000040, A007443, A007504, A010060, A030015, A050513.
%K A333176 nonn,look
%O A333176 1,1
%A A333176 _Ilya Gutkovskiy_, Mar 10 2020