A236248 Numbers m with C(2*m, m) - prime(m) prime, where C(2*m, m) = (2*m)!/(m!)^2.

2, 5, 6, 10, 29, 132, 266, 322, 350, 538, 667, 693, 776, 977, 1336, 1810, 1908, 1980, 2175, 2616, 2716, 3211, 3473, 5223, 5630, 5758, 6585, 6979, 7964, 8469, 9052, 9758, 10324, 16876, 25760, 28171

Offset: 1

Author

Zhi-Wei Sun, Jan 21 2014

Keywords

• nonn

Comments

According to the conjecture in A236256, this sequence should have infinitely many terms.

The prime C(2*a(36), a(36)) - prime(a(36)) = C(56342, 28171) - prime(28171) has 16959 decimal digits.

See A236249 for primes of the form C(2*m, m) - prime(m).

See also A236242 for a similar sequence.

Examples

			a(1) = 2 since C(2*1, 1) - prime(1) = 2 - 2 = 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..36

Crossrefs

Cf. A000040, A000984, A236241, A236242, A236245, A236249, A236256.

Programs

Mathematica

n=0;Do[If[PrimeQ[Binomial[2m,m]-Prime[m]],n=n+1;Print[n," ",m]],{m,1,10000}]