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

%I A248025 #19 Dec 23 2024 14:53:44
%S A248025 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,
%T A248025 91,12,32,52,72,92,22,42,62,82,13,43,73,14,53,83,23,54,93,33,63,94,44,
%U A248025 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
%N A248025 Lexicographically earliest permutation of the positive integers such that the first digit of a(n+1) is the digital root of a(n).
%H A248025 Reinhard Zumkeller, <a href="/A248025/b248025.txt">Table of n, a(n) for n = 1..10000</a>
%H A248025 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-September/013711.html">Fun and quick permutation (with a digital root)</a>, SeqFan list, Sep 29 2014.
%H A248025 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t A248025 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 *)
%o A248025 (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}
%o A248025 (Haskell)
%o A248025 import Data.List (delete)
%o A248025 a248025 n = a248025_list !! (n-1)
%o A248025 a248025_list = 1 : f 1 [2..] where
%o A248025   f x zs = g zs where
%o A248025     g (y:ys) = if a000030 y == a010888 x
%o A248025                then y : f y (delete y zs) else g ys
%o A248025 -- _Reinhard Zumkeller_, Sep 30 2014
%Y A248025 Cf. A010888 (digital root); similar sequences: A248024,...
%Y A248025 Cf. A247879 (inverse), A000030.
%K A248025 nonn,base
%O A248025 1,2
%A A248025 _Eric Angelini_ and _M. F. Hasler_, Sep 29 2014