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%I #17 Jun 04 2023 23:50:53
%S 2,4,4,6,10,20,36,4,24,10,28,6,44,32,54,98,64,20,174,76,110,84,72,66,
%T 68,102,300,74,62,104,230,176,108,126,124,96,38,70,48,228,240,38,196,
%U 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
%N a(n) = (least prime > binomial(2n, n)) - (greatest prime < binomial(2n, n)).
%F a(n) = A359292(n) - A359293(n-1).
%e 5 < 6 < 7, so a(2) = 7 - 5 = 2;
%e 19 < 20 < 23, so a(3) = 23 - 19 = 4;
%e 67 < 70 < 71, so a(4) = 71 - 67 = 4;
%e 251 < 252 < 257, so a(5) = 257 - 251 = 6.
%t t = Table[Binomial[2 n, n], {n, 1, 70}];
%t u = NextPrime[t]; v = Rest[NextPrime[t, -1]];
%t Rest[u] - v
%o (PARI) a(n) = my(c=binomial(2*n,n)); nextprime(c+1) - precprime(c-1); \\ _Michel Marcus_, Dec 24 2022
%Y Cf. A000040, A000984, A359292, A359293.
%K nonn
%O 2,1
%A _Clark Kimberling_, Dec 24 2022