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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 (list; graph; refs; listen; history; text; internal format)
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.
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

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)