This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159987 #20 Jan 26 2021 04:02:22 %S A159987 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, %T A159987 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, %U A159987 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 %N A159987 Catalan numbers read modulo 8. %H A159987 Rob Burns, <a href="https://arxiv.org/abs/1611.03705">Asymptotic density of Catalan numbers modulo 3 and powers of 2</a>, arXiv:1611.03705 [math.NT], 2016. %H A159987 Shu-Chung Liu and Jean C.-C. Yeh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Liu2/liu6.html">Catalan numbers modulo 2^k</a>, J. Int. Seq., Vol. 13 (2010), Article 10.5.4. %F A159987 a(n) = A000108(n) mod 8. %F A159987 a(n) == A159981(n) (mod 4). - _R. J. Mathar_, Apr 30 2009 %F A159987 Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = 0 (Burns, 2016). - _Amiram Eldar_, Jan 26 2021 %p A159987 A000108 := proc(n) binomial(2*n,n)/(n+1) ; end: %p A159987 A159987 := proc(n) A000108(n) mod 8 ; end: %p A159987 seq(A159987(n),n=0..120) ; # _R. J. Mathar_, Apr 30 2009 %t A159987 Table[Mod[CatalanNumber[n], 8], {n, 0, 100}] (* _Amiram Eldar_, Jan 26 2021 *) %Y A159987 Cf. A000108, A159981. %K A159987 easy,nonn %O A159987 0,3 %A A159987 _Philippe Deléham_, Apr 28 2009