OFFSET
1,2
COMMENTS
This sequence is the variant of A266195 in base 10.
This sequence is a permutation of the natural numbers, with inverse A306466. Proof:
- we can always extend the sequence with a power of ten not yet in the sequence, hence the sequence is well defined and infinite,
- for any k > 0, 10^(k-1) is the first k-digit number appearing in the sequence,
- all powers of ten appear in the sequence, in increasing order,
- a power of ten is always followed by the least number unused so far,
hence every number eventually appears. QED
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A306465
Rémy Sigrist, Colored logarithmic scatterplot of the sequence for n = 1..200000 (where the color is function of A054055(a(n)))
FORMULA
EXAMPLE
The first terms, alongside their digital sum and the digital sum of the product with the next term, are:
n a(n) ds(a(n)) ds(a(n)*a(n+1))
-- ---- -------- ---------------
1 1 1 2
2 2 2 6
3 3 3 3
4 10 1 4
5 4 4 8
6 11 2 10
7 5 5 5
8 100 1 6
9 6 6 12
10 101 2 14
11 7 7 14
12 110 2 16
13 8 8 24
14 111 3 27
15 9 9 9
16 1000 1 3
17 12 3 12
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 17 2019
STATUS
approved