|
|
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);
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|