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

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

Author

Reinhard Zumkeller, May 16 2005

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A000040, A067317.

Programs

Maple

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

Mathematica

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

Extensions

Corrected and extended by Emeric Deutsch, Aug 27 2007