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A113305
Primes that do not divide any central trinomial coefficient, A002426.
4
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
Nadav Kohen, Uniform Recurrence in the Motzkin Numbers and Related Sequences mod p, arXiv:2403.00149 [math.CO], 2024.
Nadav Kohen, The Automatic Study of Constant Term Sequences Modulo Prime Powers, Ph. D. Thesis, Indiana Univ. ProQuest (2025) 32282826. See pp. 45, 119.
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 24 2005
STATUS
approved