A159987 - OEIS

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A159987

Catalan numbers read modulo 8.

1, 1, 2, 5, 6, 2, 4, 5, 6, 6, 4, 2, 4, 4, 0, 5, 6, 6, 4, 6, 4, 4, 0, 2, 4, 4, 0, 4, 0, 0, 0, 5, 6, 6, 4, 6, 4, 4, 0, 6, 4, 4, 0, 4, 0, 0, 0, 2, 4, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 6, 6, 4, 6, 4, 4, 0, 6, 4, 4, 0, 4, 0, 0, 0, 6, 4, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 4, 0, 0, 0, 4, 0

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

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..104.

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.

FORMULA

a(n) = A000108(n) mod 8.

a(n) == A159981(n) (mod 4). - R. J. Mathar, Apr 30 2009

Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = 0 (Burns, 2016). - Amiram Eldar, Jan 26 2021

MAPLE