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A289682
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Catalan numbers read modulo 16.
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1
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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
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OFFSET
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0,3
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COMMENTS
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Conjecture: a(2^n-1) = 13 and a(2^n) = 6 for n >= 3. - Robert Israel, Jul 09 2017
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LINKS
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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.
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FORMULA
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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
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MAPLE
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seq ( modp(A000108(n), 16), n=0..120) ;
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MATHEMATICA
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Table[Mod[CatalanNumber[n], 16], {n, 0, 100}] (* Vincenzo Librandi, Jul 10 2017 *)
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PROG
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(PARI) a(n) = (binomial(2*n, n)/(n+1)) % 16; \\ Michel Marcus, Jul 09 2017
(MAGMA) [Catalan(n) mod 16: n in [0..100]]; // Vincenzo Librandi, Jul 10 2017
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CROSSREFS
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Cf. A000108, A036987 (mod 2), A073267 (mod 4), A159987 (mod 8).
Cf. A048881 (2-adic valuation of A000108).
Sequence in context: A279958 A348881 A324982 * A151854 A146526 A120626
Adjacent sequences: A289679 A289680 A289681 * A289683 A289684 A289685
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KEYWORD
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nonn,easy
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AUTHOR
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R. J. Mathar, Jul 09 2017
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STATUS
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approved
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