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

%I #13 Nov 24 2018 16:33:57

%S 2,3,7,11,71,127,463,3433,2704157,20058301,17672631901,35345263801,

%T 2104098963721,16123801841551,6892620648693261354601,

%U 51913710643776705684835561,410795449442059149332177041

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

%C The corresponding values of n are in A067366.

%H Harvey P. Dale, <a href="/A066749/b066749.txt">Table of n, a(n) for n = 1..53</a> (* The next term, a(54), has 1244 digits. *)

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

%t For[ n=0, True, n++, If[ PrimeQ[ z=Binomial[ n, Floor[ n/2 ] ]+1 ], Print[ z ] ] ]

%t Select[Table[1+Binomial[n,Floor[n/2]],{n,100}],PrimeQ] (* _Harvey P. Dale_, Nov 24 2018 *)

%o (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

%Y Cf. A001405, A067366.

%K nonn

%O 1,1

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

%E Repetitions removed by _N. J. A. Sloane_, Apr 09 2008