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A289682 Catalan numbers read modulo 16. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: a(2^n-1) = 13 and a(2^n) = 6 for n >= 3. - Robert Israel, Jul 09 2017

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.

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

MAPLE

seq ( modp(A000108(n), 16), n=0..120) ;

MATHEMATICA

Table[Mod[CatalanNumber[n], 16], {n, 0, 100}] (* Vincenzo Librandi, Jul 10 2017 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jul 09 2017

STATUS

approved

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Last modified May 27 11:19 EDT 2022. Contains 354096 sequences. (Running on oeis4.)