A236245 Primes of the form C(2*m, m) + prime(m), where C(2*m, m) = (2*m)!/(m!)^2.

263, 937, 3449, 12889, 2704193, 10400641, 35345263867, 23623985175715118288974865541854103729347, 362048725489728431058442528694228154899210914562190067

Offset: 1

Author

Zhi-Wei Sun, Jan 20 2014

Keywords

• nonn

Comments

Although the primes in this sequence are very rare, by the conjecture in A236241 there should be infinitely many such primes.

See A236242 for a list of known numbers m with C(2*m, m) + prime(m) prime.

Examples

			a(1) = 263 since C(2*5, 5) + prime(5) = 252 + 11 = 263 is prime, and those C(2*m, m) + prime(m) with 0 < m < 5 are composite.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A000040, A000984, A236241, A236242.

Programs

Mathematica

s[n_]:=Binomial[2n,n]+Prime[n]
a[n_]:=s[A236242(n)]
Table[a[n],{n,1,40}]