A066749 List of primes p which are equal to a central binomial coefficient C(n,floor(n/2)) plus 1.

2, 3, 7, 11, 71, 127, 463, 3433, 2704157, 20058301, 17672631901, 35345263801, 2104098963721, 16123801841551, 6892620648693261354601, 51913710643776705684835561, 410795449442059149332177041

Offset

1,1

Comments

The corresponding values of n are in A067366.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..53 (* The next term, a(54), has 1244 digits. *)

Example

For n=5 the central binomial coefficient is C(5,2)=10. Since 10+1=11 is prime, it is in the sequence.

Mathematica

For[ n=0, True, n++, If[ PrimeQ[ z=Binomial[ n, Floor[ n/2 ] ]+1 ], Print[ z ] ] ]
Select[Table[1+Binomial[n, Floor[n/2]], {n, 100}], PrimeQ] (* Harvey P. Dale, Nov 24 2018 *)

Prog

(MuPAD) for n from 0 to 200 do p := binomial(n, floor(n/2))+1: if isprime(p) then print(p) end_if end_for

Crossrefs

Cf. A001405, A067366.

Sequence in context: A073609 A267091 A053781 * A306786 A137767 A191704

Adjacent sequences: A066746 A066747 A066748 * A066750 A066751 A066752

Keyword

nonn

Author

Frank Buss (fb(AT)frank-buss.de), Jan 16 2002

Extensions

Repetitions removed by N. J. A. Sloane, Apr 09 2008

Status

approved