A067316 a(n) is the number of values of j, 0 <= j <= n, such that 1 + binomial(n,j) is prime.

1, 2, 3, 2, 5, 4, 4, 2, 5, 6, 6, 6, 6, 4, 5, 2, 6, 8, 8, 6, 6, 4, 4, 2, 11, 4, 4, 8, 8, 8, 4, 2, 6, 4, 8, 14, 8, 4, 5, 6, 12, 10, 4, 6, 9, 8, 8, 4, 6, 8, 6, 10, 6, 6, 12, 6, 8, 4, 12, 2, 6, 8, 4, 2, 8, 18, 8, 2, 6, 14, 10, 16, 10, 6, 4, 10, 13, 8, 12, 4, 8, 2, 8, 14, 2, 6, 4, 10, 10, 16, 10, 10, 9

Offset: 0

Author

Labos Elemer, Jan 15 2002

Keywords

• nonn

Examples

			For n = 8, the primes are 2, 29, 71, 29, 2, so a(n) = 5.
a(n) = 6 for n = 9, 10, 11, 12. Also, a(n) = 10 for n = 149, ..., 154.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A066699, A067317.

Programs

Mathematica

a[n_] := Count[Table[PrimeQ[Binomial[n, w]+1], {w, 0, n}], True]

PARI

a(n) = sum(j=0, n, isprime(1 + binomial(n,j))); \\ Michel Marcus, Oct 30 2018

PARI

a(n) = 2 * sum(k=0, (n-1)\2, isprime(binomial(n, k) + 1)) + if(!(n%2), isprime(binomial(n, n/2) + 1)); \\ Amiram Eldar, Jul 18 2024