A119246 Numbers containing in decimal representation their digital root.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 20, 29, 30, 39, 40, 49, 50, 59, 60, 69, 70, 79, 80, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 109, 118, 127, 128, 136, 138, 145, 148, 154, 158, 163, 168, 172, 178, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 198, 199, 200

Offset: 1

Author

Reinhard Zumkeller, May 10 2006

Keywords

• nonn
• base

Comments

Complement of A119247.

For terms u: all digital permutations of u form terms; u*10 and all insertions of 0 are terms; if v is another term, then the concatenations uv, vu are also terms, as well as all insertions of v in u; these properties allow the construction of all terms beginning with {d:1<=d<=9}. - Reinhard Zumkeller, May 19 2006

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Digital Root

Crossrefs

Cf. A010888.

Cf. A052018, A031298, A138166.

Programs

Haskell

a119246 n = a119246_list !! (n-1)
a119246_list =
    filter (\x -> a010888 x `elem` a031298_row (fromInteger x)) [0..]
-- Reinhard Zumkeller, Dec 16 2013, Apr 14 2011

Mathematica

d[n_] := IntegerDigits[n]; Select[Range[0, 200], MemberQ[d[#1], NestWhile[Total[d[#]] &, #1, # > 9 &]] &] (* Jayanta Basu, Jul 13 2013 *)