A359294 a(n) = (least prime > binomial(2n, n)) - (greatest prime < binomial(2n, n)).

2, 4, 4, 6, 10, 20, 36, 4, 24, 10, 28, 6, 44, 32, 54, 98, 64, 20, 174, 76, 110, 84, 72, 66, 68, 102, 300, 74, 62, 104, 230, 176, 108, 126, 124, 96, 38, 70, 48, 228, 240, 38, 196, 210, 38, 260, 466, 72, 60, 36, 250, 156, 50, 46, 102, 84, 26, 240, 372, 90, 54, 360, 50, 276, 314, 408, 32, 168, 164

Offset

2,1

Links

Table of n, a(n) for n=2..70.

Formula

a(n) = A359292(n) - A359293(n-1).

Example

     5 < 6 < 7, so a(2) = 7 - 5 = 2;
   19 < 20 < 23, so a(3) = 23 - 19 = 4;
   67 < 70 < 71, so a(4) = 71 - 67 = 4;
  251 < 252 < 257, so a(5) = 257 - 251 = 6.

Mathematica

t = Table[Binomial[2 n, n], {n, 1, 70}];
u = NextPrime[t]; v = Rest[NextPrime[t, -1]];
Rest[u] - v

Prog

(PARI) a(n) = my(c=binomial(2*n, n)); nextprime(c+1) - precprime(c-1); \\ Michel Marcus, Dec 24 2022

Crossrefs

Cf. A000040, A000984, A359292, A359293.

Sequence in context: A340626 A351489 A022471 * A224487 A185342 A276985

Adjacent sequences: A359291 A359292 A359293 * A359295 A359296 A359297

Keyword

nonn

Author

Clark Kimberling, Dec 24 2022

Status

approved