A130856 The digital root (A010888) of the Catalan numbers A000108.

1, 1, 2, 5, 5, 6, 6, 6, 8, 2, 2, 7, 4, 4, 9, 9, 9, 6, 6, 6, 3, 3, 3, 9, 9, 9, 8, 2, 2, 4, 1, 1, 3, 3, 3, 1, 7, 7, 2, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 3, 3, 3, 9, 9, 9, 3, 3, 3, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 2, 2, 4, 1, 1, 3

Offset

0,3

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Maple

A130856 := proc(n) option remember: if(n=0)then return 1:fi: return ((add(procname(k)*procname(n-1-k), k=0..n-1)-1) mod 9) + 1 end: seq(A130856(n), n=0..100); # Nathaniel Johnston, May 05 2011

Mathematica

droot[n_]:=NestWhile[Total[IntegerDigits[#]]&, n, #>9&]; droot/@CatalanNumber[ Range[ 0, 100]] (* Harvey P. Dale, Apr 09 2022 *)

Prog

(PARI) a(n) = (binomial(2*n, n)/(n+1)-1)%9 + 1; \\ Michel Marcus, Nov 28 2022

Crossrefs

Cf. A000108, A010888, A130851.

Sequence in context: A073101 A235526 A130851 * A004095 A145434 A220426

Adjacent sequences: A130853 A130854 A130855 * A130857 A130858 A130859

Keyword

nonn,easy,base

Author

N. J. A. Sloane, Aug 21 2007

Extensions

Name corrected by Nathaniel Johnston, May 05 2011

Status

approved