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%I A284030 #32 Sep 08 2023 01:12:15
%S A284030 1,2,3,4,5,6,7,8,9,19,18,28,17,11,26,37,16,46,55,29,15,12,25,64,24,13,
%T A284030 33,14,23,38,27,73,32,82,47,56,41,42,22,65,31,91,21,39,48,118,49,74,
%U A284030 57,66,35,83,34,43,75,84,92,44,119,58,52,59,51,67,127,76,128,137,146,69,68,93,136,36,145,155,154,111,45,85,53,163,172,62,94,54,61,112,77,79,78,87,129,86,71,138,147
%N A284030 Replacing each term with its digital root generates the original sequence, digit by digit.
%C A284030 The sequence is started with a(1) = 1 and always extended with the smallest integer not yet present and not leading to a contradiction.
%C A284030 There is no digit "0" in the sequence as "0" cannot be a digital root.
%H A284030 Jean-Marc Falcoz, <a href="/A284030/b284030.txt">Table of n, a(n) for n = 1..10001</a>
%e A284030 After 1,2,3,4,5,6,7,8,9 we have the terms 19,18,28,17,11,26,37,16,46,55,..., whose digital roots are respectively 1,9,1,8,2,8,1,7,1,1,... These digits are precisely the ones used in the sequence, in that order.
%t A284030 Dig[n_]:=NestWhile[Total@IntegerDigits@#&,n,#>9&];a[1]=1;a[n_]:=a[n]=(k=1;While[MemberQ[IntegerDigits@k,0]||MemberQ[s=Array[a,n-1],k]||Dig@k!=Flatten[IntegerDigits/@Join[s,{k}]][[n]],k++];k);
%t A284030 Array[a,100] (* _Giorgos Kalogeropoulos_, Sep 07 2023 *)
%Y A284030 Cf. A010888 (digital root), A052382 (zeroless numbers).
%K A284030 base,nonn
%O A284030 1,2
%A A284030 _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 24 2017

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