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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). 6

%I #18 Jan 02 2023 12:30:50

%S 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 91,12,32,52,72,92,22,42,62,82,13,43,73,14,53,83,23,54,93,33,63,94,44,

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

%H Reinhard Zumkeller, <a href="/A248025/b248025.txt">Table of n, a(n) for n = 1..10000</a>

%H E. Angelini, <a href="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 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%t 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 (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 (Haskell)

%o import Data.List (delete)

%o a248025 n = a248025_list !! (n-1)

%o a248025_list = 1 : f 1 [2..] where

%o f x zs = g zs where

%o g (y:ys) = if a000030 y == a010888 x

%o then y : f y (delete y zs) else g ys

%o -- _Reinhard Zumkeller_, Sep 30 2014

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

%Y Cf. A247879 (inverse), A000030.

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _M. F. Hasler_, Sep 29 2014

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)