%I #17 Jul 18 2024 09:18:35

%S 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,

%T 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,

%U 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

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

%H Amiram Eldar, <a href="/A067316/b067316.txt">Table of n, a(n) for n = 0..10000</a>

%e For n = 8, the primes are 2, 29, 71, 29, 2, so a(n) = 5.

%e a(n) = 6 for n = 9, 10, 11, 12. Also, a(n) = 10 for n = 149, ..., 154.

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

%o (PARI) a(n) = sum(j=0, n, isprime(1 + binomial(n,j))); \\ _Michel Marcus_, Oct 30 2018

%o (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

%Y Cf. A066699, A067317.

%K nonn

%O 0,2

%A _Labos Elemer_, Jan 15 2002