A236245 Primes of the form C(2*m, m) + prime(m), where C(2*m, m) = (2*m)!/(m!)^2.

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

Zhi-Wei Sun, Table of n, a(n) for n = 1..25

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

Cf. A000040, A000984, A236241, A236242.

Sequence in context: A245877 A142379 A128654 * A343192 A023314 A054802

Adjacent sequences: A236242 A236243 A236244 * A236246 A236247 A236248

Keyword

nonn

Author

Zhi-Wei Sun, Jan 20 2014

Status

approved