A331117 - OEIS

%I #18 Jan 13 2020 20:59:38

%S 1,2,3,6,4,5,10,11,12,13,16,17,24,7,14,15,20,8,9,18,19,28,21,22,23,26,

%T 25,30,33,36,39,48,27,34,37,44,29,38,41,42,31,32,35,40,43,46,45,50,55,

%U 60,47,54,59,68,49,58,63,66,51,56,61,62,52,57,64,53,65,70,77,84,67,74,81,82,69,78,85,90,99,108,109

%N Lexicographically earliest sequence of distinct terms such that a(n+1) = a(n) + the largest odd digit of a(n), starting with a(n) = 1. If this addition is impossible, or if it leads to a term already in the sequence, restart the sequence from there with the smallest unused integer.

%C This sequence is a permutation of the positive integers.

%H Carole Dubois, <a href="/A331117/b331117.txt">Table of n, a(n) for n = 1..5000</a>

%e a(1) = 1

%e a(2) = a(1) + 1 = 2;

%e as a(2) = 2 has no odd digit, we restart the sequence with a(3) = 3;

%e a(4) = a(3) + 3 = 6;

%e as a(4) = 6 has no odd digit, we restart the sequence with a(5) = 4;

%e as a(5) = 4 has no odd digit, we restart the sequence with a(6) = 5;

%e a(6) = a(5) + 5 = 10;

%e a(7) = a(6) + 1 = 11;

%e a(8) = a(7) + 1 = 12;

%e a(9) = a(8) + 1 = 13;

%e a(10) = a(9) + 3 = 16; etc.

%t Nest[Append[#1, If[FreeQ[#1, #2], #2, Block[{k = 2}, While[! FreeQ[#1, k], k++]; k]] ] & @@ {#1, If[Length@ #2 > 0, #1[[-1]] + #2[[-1]], 1]} & @@ {#, Select[Union@ IntegerDigits[#[[-1]] ], OddQ]} &, {1}, 80] (* _Michael De Vlieger_, Jan 11 2020 *)

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Carole Dubois_, Jan 10 2020