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
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
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<