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%I #10 Apr 12 2014 13:15:02
%S 263,937,3449,12889,2704193,10400641,35345263867,
%T 23623985175715118288974865541854103729347,
%U 362048725489728431058442528694228154899210914562190067
%N Primes of the form C(2*m, m) + prime(m), where C(2*m, m) = (2*m)!/(m!)^2.
%C Although the primes in this sequence are very rare, by the conjecture in A236241 there should be infinitely many such primes.
%C See A236242 for a list of known numbers m with C(2*m, m) + prime(m) prime.
%H Zhi-Wei Sun, <a href="/A236245/b236245.txt">Table of n, a(n) for n = 1..25</a>
%e 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.
%t s[n_]:=Binomial[2n,n]+Prime[n]
%t a[n_]:=s[A236242(n)]
%t Table[a[n],{n,1,40}]
%Y Cf. A000040, A000984, A236241, A236242.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 20 2014
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