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A340138 a(1)=0, a(n+1) = the least m not already in the sequence such that the decimal digital root r of a(n-1) is found somewhere among the decimal digits of m.

%I A340138 #9 Jan 29 2021 19:14:57
%S A340138 0,10,1,11,2,12,3,13,4,14,5,15,6,16,7,17,8,18,9,19,21,23,25,27,29,20,
%T A340138 22,24,26,28,31,34,37,41,35,38,32,45,39,30,33,36,49,40,42,46,51,56,52,
%U A340138 47,62,48,43,57,53,58,44,68,50,54,59,55,61,67,64,71,78,60
%N A340138 a(1)=0, a(n+1) = the least m not already in the sequence such that the decimal digital root r of a(n-1) is found somewhere among the decimal digits of m.
%C A340138 a(n) = 10^k occurs before n = 10^k for 0 < k <= 5.
%C A340138 Conjecture: permutation of the nonnegative numbers.
%C A340138 A decimal version of A339607, a permutation of the integers having to do with binary weight, but instead using digital root rather than digit sum. The plots of these sequences have similar features.
%H A340138 Michael De Vlieger, <a href="/A340138/b340138.txt">Table of n, a(n) for n = 1..10000</a>
%H A340138 Michael De Vlieger, <a href="/A340138/a340138.png">Plot (n, a(n)) for 1 <= n <= 10^3</a> with records in dark red and least unused numbers in dark blue, with records of a(n)-n in red, many labeled, and records of n-a(n) in blue, many labeled.
%H A340138 Michael De Vlieger, <a href="/A340138/a340138_1.png">Logarithmic plot (n, a(n)-n) for 1 <= n <= 10^5</a> with records labeled in red, records of n-a(n) labeled in blue, and zeros plotted in black.
%t A340138 Block[{a = {0, 10}, k, r}, Do[k = 1; r = # + 9 Boole[# == 0] &@ Mod[a[[-1]], 9]; While[Nand[FreeQ[a, k], ! FreeQ[IntegerDigits[k], r]], k++]; AppendTo[a, k], 66]; a]
%Y A340138 Cf. A248025, A338191, A339607.
%K A340138 nonn,base
%O A340138 1,2
%A A340138 _Michael De Vlieger_, Jan 21 2021