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Primes of the form C(2*m, m) - prime(m), where C(2*m, m) = (2*m)!/(m!)^2.
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%I #14 Jan 21 2014 07:57:21

%S 3,241,911,184727,30067266499540931,

%T 1454272161238683681127450712107767894181359647011258114106151524833563647084221

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

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

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

%C See also A236245 for a similar sequence.

%H Zhi-Wei Sun, <a href="/A236249/b236249.txt">Table of n, a(n) for n = 1..12</a>

%e 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.

%t t[n_]:=Binomial[2n,n]-Prime[n]

%t a[n_]:=t[A234248(n)]

%t Table[a[n],{n,1,6}]

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 21 2014