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

1,3

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A010888.

Cf. A052018, A031298, A138166.

Sequence in context: A321767 A207506 A343131 * A280657 A117241 A108191

Adjacent sequences: A119243 A119244 A119245 * A119247 A119248 A119249

Keyword

nonn,base

Author

Reinhard Zumkeller, May 10 2006

Status

approved