A061598 Distance to the largest Catalan number which is less than, but divides the n-th Catalan number; i.e., a(n) gives minimum k (> 0) such that C_{n-k}|C_n.

1, 1, 2, 2, 1, 4, 6, 5, 7, 8, 7, 8, 10, 11, 12, 13, 14, 12, 14, 12, 18, 19, 20, 22, 20, 22, 23, 24, 25, 26, 30, 27, 28, 29, 31, 32, 33, 34, 35, 36, 35, 36, 38, 39, 40, 41, 42, 38, 39, 43, 45, 46, 47, 49, 53, 54, 55, 55, 57, 55, 52, 53, 56, 61, 62, 60, 62, 62, 63, 64, 68, 64, 65

Offset

1,3

Links

Table of n, a(n) for n=1..73.

Example

a(5) = 1 because C_4 (= 14) divides C_5 (= 42).

Maple

[seq(WCD(j), j=1..100)]; WCD := proc(n) local i; for i from n-1 by -1 to 0 do if(0 = (`mod`(Cat(n), Cat(i)))) then RETURN(n-i); fi; od; end; Cat := n -> (binomial(2*n, n)/(n+1));

Mathematica

a[n_] := For[k = n - 1, True, k--, If[Divisible[CatalanNumber[n], CatalanNumber[k]], Return[n - k]]]; a[1] = 1; Array[a, 100] (* Jean-François Alcover, Mar 06 2016 *)

Crossrefs

Cf. A000108.

Sequence in context: A363493 A193597 A191490 * A328873 A071946 A053495

Adjacent sequences: A061595 A061596 A061597 * A061599 A061600 A061601

Keyword

nonn

Author

Antti Karttunen, Jun 13 2001

Status

approved