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

%I A067316 #17 Jul 18 2024 09:18:35
%S A067316 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 A067316 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 A067316 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 A067316 a(n) is the number of values of j, 0 <= j <= n, such that 1 + binomial(n,j) is prime.
%H A067316 Amiram Eldar, <a href="/A067316/b067316.txt">Table of n, a(n) for n = 0..10000</a>
%e A067316 For n = 8, the primes are 2, 29, 71, 29, 2, so a(n) = 5.
%e A067316 a(n) = 6 for n = 9, 10, 11, 12. Also, a(n) = 10 for n = 149, ..., 154.
%t A067316 a[n_] := Count[Table[PrimeQ[Binomial[n, w]+1], {w, 0, n}], True]
%o A067316 (PARI) a(n) = sum(j=0, n, isprime(1 + binomial(n,j))); \\ _Michel Marcus_, Oct 30 2018
%o A067316 (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 A067316 Cf. A066699, A067317.
%K A067316 nonn
%O A067316 0,2
%A A067316 _Labos Elemer_, Jan 15 2002