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URL: https://oeis.org/A327689

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A327689
Lexicographically earliest sequence of distinct positive terms such that for any k > 0, the sum of the first k digits does not exceed k.
1
1, 10, 2, 11, 100, 3, 101, 12, 102, 110, 20, 21, 111, 1000, 4, 1001, 13, 1002, 103, 1003, 1010, 22, 1011, 112, 1012, 1020, 120, 121, 1021, 1100, 30, 200, 31, 1101, 201, 202, 1102, 1110, 210, 211, 1111, 10000, 5, 10001, 14, 10002, 104, 10003, 1004, 10004, 10010
OFFSET
1,2
COMMENTS
The sequence is a permutation of the natural numbers:
- we can always extend the sequence with a power of 10 that has not yet appeared,
- every power of 10 appears in the sequence,
- for any n > 0 with digital sum s: n can appear after any number of the form 10^k with k+1 >= s, hence n will eventually appear.
FORMULA
Sum_{i = 1..n} A007953(a(n)) <= Sum_{i = 1..n} A055642(a(n)).
EXAMPLE
The first terms, alongside the corresponding digits and sum of digits, are:
n a(n) k d(k) s(k)
-- ---- -- ---- ----
1 1 1 1 1
2 10 2 1 2
3 0 2
3 2 4 2 4
4 11 5 1 5
6 1 6
5 100 7 1 7
8 0 7
9 0 7
6 3 10 3 10
PROG
(PARI) See Links section.
CROSSREFS
Sequence in context: A269631 A334737 A334837 * A317387 A303784 A278649
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Sep 22 2019
STATUS
approved