A236248 - OEIS

%I #27 Jan 22 2014 09:00:04

%S 2,5,6,10,29,132,266,322,350,538,667,693,776,977,1336,1810,1908,1980,

%T 2175,2616,2716,3211,3473,5223,5630,5758,6585,6979,7964,8469,9052,

%U 9758,10324,16876,25760,28171

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

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

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

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

%C See also A236242 for a similar sequence.

%H Zhi-Wei Sun, <a href="/A236248/b236248.txt">Table of n, a(n) for n = 1..36</a>

%e 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.

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

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 21 2014