A113305 Primes that do not divide any central trinomial coefficient, A002426.

2, 5, 11, 13, 23, 29, 31, 37, 53, 59, 61, 67, 71, 79, 83, 89, 97, 101, 103, 127, 137, 139, 149, 151, 157, 163, 167, 181, 197, 211, 223, 227, 229, 239, 241, 251, 257, 263, 271, 313, 317, 331, 337, 349, 353, 359, 367, 379, 389, 397, 431, 433, 449, 461, 463, 479

Offset: 1

Author

T. D. Noe, Oct 24 2005

Keywords

• nonn

Comments

For primes less than 10^6, the density of these primes is near 0.6075.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1600
• Nadav Kohen, Uniform Recurrence in the Motzkin Numbers and Related Sequences mod p, arXiv:2403.00149 [math.CO], 2024.
• Narad Rampersad and Jeffrey Shallit, Congruence properties of combinatorial sequences via Walnut and the Rowland-Yassawi-Zeilberger automaton, arXiv:2110.06244 [math.CO], 2021.

Crossrefs

Cf. A113302 (number of k for which prime(n) divides T(k)), A113303 (least k such that prime(n) divides T(k)).

Programs

Mathematica

nn=1000; a=b=1; t=Join[{1}, Table[c=((2n-1)b+3(n-1)a)/n; a=b; b=c; c, {n, 2, nn}]]; pLst={}; Do[p=Prime[n]; k=1; While[k
0, k++ ]; If[k==p, AppendTo[pLst, p]], {n, PrimePi[nn]}]; pLst