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A284030 Replacing each term with its digital root generates the original sequence, digit by digit. 1
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, 33, 14, 23, 38, 27, 73, 32, 82, 47, 56, 41, 42, 22, 65, 31, 91, 21, 39, 48, 118, 49, 74, 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 (list; graph; refs; listen; history; text; internal format)
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
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
Cf. A010888 (digital root), A052382 (zeroless numbers).
Sequence in context: A118758 A174025 A106649 * A087121 A087052 A077557
KEYWORD
base,nonn
AUTHOR
STATUS
approved

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)