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

0,5

Links

Table of n, a(n) for n=0..85.

Formula

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

Example

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.

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}]

Prog

(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

Crossrefs

Cf. A007318, A008949, A258483, A382816.

Sequence in context: A357458 A349277 A390279 * A307014 A240871 A236765

Adjacent sequences: A382814 A382815 A382816 * A382818 A382819 A382820

Keyword

nonn

Author

Clark Kimberling, Apr 07 2025

Status

approved