A135785 Union of A000040, A001248 and A037074.

2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Vladimir Shevelev, May 10 2008, May 16 2008

Keywords

• nonn

Comments

a(n) possesses the following property: every i not exceeding a(n)/2 for which (a(n),i)>1 does not divide binomial(a(n)-i-1,i-1). Numbers with this property are called "binomial primes". There exist only nine binomial primes which are not terms of this sequence:1,6,8,10,12,20,21,24,33.

Links

• V. Shevelev, On divisibility of binomial(n-i-1,i-1) by i, Int. J. of Number Theory, 3, no.1 (2007), 119-139.

Crossrefs

Cf. A138389, A000040, A001248, A037074.

Programs

Mathematica

aQ[n_] := PrimeQ[n] || (PrimeNu[n]<3 && Module[{p = FactorInteger[n][[1,1]]}, n==p^2 || (n==p(p+2) && PrimeQ[p+2])]); Select[Range[2, 250], aQ] (* Amiram Eldar, Dec 04 2018 *)

PARI

isok(n) = isprime(n) || (issquare(n) && isprime(sqrtint(n))) || (issquare(n+1) && isprime(sqrtint(n+1)-1) && isprime(sqrtint(n+1)+1)); \\ Michel Marcus, Dec 04 2018

Extensions

Missing 47 and more terms from Michel Marcus, Dec 04 2018