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A236245
Primes of the form C(2*m, m) + prime(m), where C(2*m, m) = (2*m)!/(m!)^2.
6
263, 937, 3449, 12889, 2704193, 10400641, 35345263867, 23623985175715118288974865541854103729347, 362048725489728431058442528694228154899210914562190067
OFFSET
1,1
COMMENTS
Although the primes in this sequence are very rare, by the conjecture in A236241 there should be infinitely many such primes.
See A236242 for a list of known numbers m with C(2*m, m) + prime(m) prime.
LINKS
EXAMPLE
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.
MATHEMATICA
s[n_]:=Binomial[2n, n]+Prime[n]
a[n_]:=s[A236242(n)]
Table[a[n], {n, 1, 40}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 20 2014
STATUS
approved