A067317 -id:A067317 - cp's OEIS frontend

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

Labos Elemer, Jan 15 2002

nonn

			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.

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

Cf. A066699, A067317.

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

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

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

A106790 Smallest k>0 such that binomial(n,k) + 1 is prime.

Original entry on oeis.org

1, 1, 3, 1, 2, 1, 7, 2, 2, 1, 4, 1, 2, 5, 15, 1, 2, 1, 4, 2, 2, 1, 23, 2, 6, 4, 4, 1, 7, 1, 31, 10, 6, 10, 4, 1, 18, 15, 9, 1, 2, 1, 17, 2, 2, 1, 23, 2, 4, 20, 6, 1, 6, 8, 10, 6, 2, 1, 59, 1, 2, 25, 63, 2, 2, 1, 67, 8, 2, 1

Offset: 1

Reinhard Zumkeller, May 16 2005

nonn

a(n) <= n; for primes p: a(p-1) = 1.
The values of n for which a(n)=n yield the sequence A067317. - Emeric Deutsch, Aug 27 2007
If a(n) > n/2 then a(n) = n. a(n) = floor(n/2) for n = 2, 5, 37, 47, 124.  Are there others? - Robert Israel, Mar 09 2020

Robert Israel, Table of n, a(n) for n = 1..4000

Cf. A000040, A067317.

a:=proc(n) local k: for k while isprime(1+binomial(n,k))=false do end do: k end proc: seq(a(n), n=1..70); # Emeric Deutsch, Aug 27 2007

a[n_] := For[k = 1, True, k++, If[PrimeQ[Binomial[n, k] + 1], Return[k]]];
Array[a, 70] (* Jean-François Alcover, Feb 13 2018 *)

Corrected and extended by Emeric Deutsch, Aug 27 2007

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI