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

Author

N. J. A. Sloane, Aug 21 2007

Keywords

• nonn
• easy
• base

Links

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

Crossrefs

Cf. A000108, A010888, A130851.

Programs

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 *)

PARI

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

Extensions

Name corrected by Nathaniel Johnston, May 05 2011