OFFSET
1,2
COMMENTS
The sequence is started with a(1) = 1 and always extended with the smallest integer not yet present and not leading to a contradiction.
There is no digit "0" in the sequence as "0" cannot be a digital root.
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001
EXAMPLE
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.
MATHEMATICA
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);
Array[a, 100] (* Giorgos Kalogeropoulos, Sep 07 2023 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Mar 24 2017
STATUS
approved