A236249 Primes of the form C(2*m, m) - prime(m), where C(2*m, m) = (2*m)!/(m!)^2.

3, 241, 911, 184727, 30067266499540931, 1454272161238683681127450712107767894181359647011258114106151524833563647084221

Offset: 1

Author

Zhi-Wei Sun, Jan 21 2014

Keywords

• nonn

Comments

Though the primes in this sequence are very rare, according to the conjecture in A236256 there should be infinitely many such primes.

See A236248 for a list of known numbers m with C(2*m, m) - prime(m) prime.

See also A236245 for a similar sequence.

Examples

			a(1) = 3 since C(2*1, 1) - prime(1) = 0 is not prime, but C(2*2, 2) - prime(2) = 6 - 3 = 3 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A000040, A000984, A236241, A236242, A236245, A236248, A236256.

Programs

Mathematica

t[n_]:=Binomial[2n,n]-Prime[n]
a[n_]:=t[A234248(n)]
Table[a[n],{n,1,6}]