A289682 Catalan numbers read modulo 16.
1, 1, 2, 5, 14, 10, 4, 13, 6, 14, 12, 2, 12, 4, 8, 13, 6, 6, 12, 6, 4, 12, 8, 2, 12, 12, 8, 4, 8, 8, 0, 13, 6, 6, 12, 14, 4, 12, 8, 6, 4, 4, 8, 12, 8, 8, 0, 2, 12, 12, 8, 12, 8, 8, 0, 4, 8, 8, 0, 8, 0, 0, 0, 13, 6, 6, 12, 14, 4, 12, 8, 14, 4, 4, 8, 12, 8, 8, 0, 6, 4, 4, 8, 4, 8, 8, 0, 12
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
- Rob Burns, Asymptotic density of Catalan numbers modulo 3 and powers of 2, arXiv:1611.03705 [math.NT], 2016.
- Shu-Chung Liu and Jean C.-C. Yeh, Catalan numbers modulo 2^k, J. Int. Seq., Vol. 13 (2010), Article 10.5.4, Theorem 5.5.
Crossrefs
Programs
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Magma
[Catalan(n) mod 16: n in [0..100]]; // Vincenzo Librandi, Jul 10 2017
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Maple
seq ( modp(A000108(n),16),n=0..120) ;
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Mathematica
Table[Mod[CatalanNumber[n], 16], {n, 0, 100}] (* Vincenzo Librandi, Jul 10 2017 *) -
PARI
a(n) = (binomial(2*n, n)/(n+1)) % 16; \\ Michel Marcus, Jul 09 2017
Formula
a(n) = A000108(n) mod 16.
Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = 0 (Burns, 2016). - Amiram Eldar, Jan 26 2021
Comments