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

1,1

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.

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<p && Mod[t[[k]], p]>0, k++ ]; If[k==p, AppendTo[pLst, p]], {n, PrimePi[nn]}]; pLst

Crossrefs

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

Sequence in context: A276660 A086081 A345707 * A095078 A335874 A062572

Adjacent sequences: A113302 A113303 A113304 * A113306 A113307 A113308

Keyword

nonn

Author

T. D. Noe, Oct 24 2005

Status

approved