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
Links
- Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Programs
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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
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Mathematica
droot[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]; droot/@CatalanNumber[ Range[ 0,100]] (* Harvey P. Dale, Apr 09 2022 *)
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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