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, 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.

Links

Table of n, a(n) for n=1..51.

Rémy Sigrist, PARI program for A327689

Index entries for sequences that are permutations of the natural numbers

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

Cf. A007953, A055642.

Sequence in context: A269631 A334737 A334837 * A317387 A303784 A278649

Adjacent sequences: A327686 A327687 A327688 * A327690 A327691 A327692

Keyword

nonn,base

Author

Rémy Sigrist, Sep 22 2019

Status

approved