A382817 a(n) = number of primes among the partial sums of row n of Pascal's triangle (A007318).

0, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 3, 2, 3, 2, 3, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 3, 0, 2, 7, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 5, 3, 3, 2, 3, 2, 3, 3, 10, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 0

Offset: 0

Author

Clark Kimberling, Apr 07 2025

Keywords

• nonn

Examples

			The numbers in A008949 (partial sums of Pascal's triangle) begin thus:
  1
  1    2
  1    3     4
  1    4     7     8
  1    5    11    15    16
  1    6    16    26    31    32
  1    7    22    42    57    63    64
Row n=4 includes exactly 2 primes, so a(4) = 2.
		

Crossrefs

Cf. A007318, A008949, A258483, A382816.

Programs

Maple

a:= n-> nops(select(isprime, ListTools[PartialSums]
            ([seq(binomial(n, k), k=0..n)]))):
seq(a(n), n=0..100);  # Alois P. Heinz, Apr 07 2025

Mathematica

t = Accumulate /@ Table[Binomial[n, i], {n, 0, 100}, {i, 0, n}]; (* A037955 *)
Map[PrimeQ, t]; Table[Count[m[[n]], True], {n, 1, 100}]

PARI

a(n) = my(v=vector(n+1, k, binomial(n,k-1))); #select(isprime, vector(#v, k, sum(i=1, k, v[i]))); \\ Michel Marcus, Apr 13 2025

Formula

a(n) = 0 <=> n in { A258483 }.