A050513 -id:A050513 - cp's OEIS frontend

A030015 Binomial transform of {1, primes}.

1, 3, 8, 21, 54, 137, 342, 837, 2006, 4713, 10882, 24771, 55764, 124465, 275934, 608283, 1334120, 2911871, 6325092, 13674121, 29425308, 63042233, 134517426, 285984131, 606056546, 1280778343, 2700105566, 5680099085, 11925792492, 24993841655, 52291456452

Offset: 0

N. J. A. Sloane

nonn

N. J. A. Sloane, Transforms

Cf. A008578, A050513.

Flatten[{1, Table[1 + Sum[Binomial[n, k]*Prime[k], {k, 1, n}], {n, 1, 30}]}] (* Vaclav Kotesovec, Oct 29 2017 *)

G.f.: Prime(x/(1-x)), Prime(x) = Sum_{n>0} A008578(n)*x^n. - Vladimir Kruchinin, Aug 11 2010

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Mar 10 2020

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

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

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

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

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

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

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

cp's OEIS Frontend

A030015 Binomial transform of {1, primes}.

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