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

Author

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

Keywords

• nonn
• base

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

Crossrefs

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

Cf. A247879 (inverse), A000030.

Programs

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

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 *)

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<