A248025 Lexicographically earliest permutation of the positive integers such that the first digit of a(n+1) is the digital root of a(n).

1, 10, 11, 2, 20, 21, 3, 30, 31, 4, 40, 41, 5, 50, 51, 6, 60, 61, 7, 70, 71, 8, 80, 81, 9, 90, 91, 12, 32, 52, 72, 92, 22, 42, 62, 82, 13, 43, 73, 14, 53, 83, 23, 54, 93, 33, 63, 94, 44, 84, 34, 74, 24, 64, 15, 65, 25, 75, 35, 85, 45, 95, 55, 16, 76, 46, 17, 86, 56, 26, 87, 66, 36, 96

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

E. Angelini, Fun and quick permutation (with a digital root), SeqFan list, Sep 29 2014.

Index entries for sequences that are permutations of the natural numbers

Mathematica

Nest[Append[#, Block[{k = 1, r = Mod[#[[-1]], 9] + 9 Boole[Mod[#[[-1]], 9] == 0]}, While[Nand[FreeQ[#, k], IntegerDigits[k][[1]] == r], k++]; k]] &, {1}, 73] (* Michael De Vlieger, Oct 15 2020 *)

Prog

(PARI) a(n, S=1, u=2)={for(i=1, n, print1(S", "); S=(S-1)%9+1; for(k=1, 9e9, bittest(u, k)&&next; S==digits(k)[1]||next; u+=1<<S=k; break)); S}
(Haskell)
import Data.List (delete)
a248025 n = a248025_list !! (n-1)
a248025_list = 1 : f 1 [2..] where
  f x zs = g zs where
    g (y:ys) = if a000030 y == a010888 x
               then y : f y (delete y zs) else g ys
-- Reinhard Zumkeller, Sep 30 2014

Crossrefs

Cf. A010888 (digital root); similar sequences: A248024,...

Cf. A247879 (inverse), A000030.

Sequence in context: A328752 A173821 A101807 * A303501 A368347 A289985

Adjacent sequences: A248022 A248023 A248024 * A248026 A248027 A248028

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Sep 29 2014

Status

approved