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

2, 3, 10, 7, 20, 23, 58, 19, 44, 51, 112, 63, 140, 151, 328, 53, 114, 117, 250, 131, 276, 287, 604, 161, 342, 355, 742, 383, 798, 825, 1720, 131, 270, 273, 566, 289, 596, 607, 1252, 323, 664, 675, 1392, 711, 1458, 1481, 3046, 407, 832, 839, 1718, 875, 1782

Offset: 1

Author

Ilya Gutkovskiy, Mar 10 2020

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A007443, A007504, A010060, A030015, A050513.

Programs

Maple

N:= 200: # for a(1) .. a(N)
P:= [seq(ithprime(i),i=1..N)]:
B:= [1,1]: R:= 2:
for n from 2 to N do
  B:= [1,op(B[2..-1]+B[1..-2] mod 2),1];
  R:= R, convert(P[select(t -> B[t+1] = 1,[$1..n])],`+`);
od:
R; # Robert Israel, Jan 29 2025

Mathematica

Table[Sum[Mod[Binomial[n, k], 2] Prime[k], {k, 1, n}], {n, 1, 53}]

PARI

a(n) = sum(k=1, n, if (binomial(n, k) % 2, prime(k))); \\ Michel Marcus, Mar 10 2020

Python

from sympy import prime
def A333176(n): return sum(prime(k) for k in range(1,n+1) if not ~n&k) # Chai Wah Wu, Jul 22 2025

Formula

Sum_{k=1..n} (-1)^A010060(n-k) * (binomial(n,k) mod 2) * a(k) = prime(n).