A328754 Lexicographically earliest sequence of distinct positive numbers such that for any n > 0, the first nonzero digit of a(n+1)/a(n) is "3".

1, 3, 9, 27, 10, 30, 11, 4, 12, 36, 13, 5, 15, 45, 14, 42, 16, 6, 2, 7, 21, 8, 24, 72, 22, 66, 20, 60, 18, 54, 17, 51, 19, 57, 171, 52, 156, 47, 141, 43, 129, 39, 117, 37, 111, 34, 102, 31, 93, 28, 84, 26, 78, 25, 75, 23, 69, 207, 63, 189, 58, 174, 53, 159, 48

Offset

1,2

Comments

In other words, for any n > 0, we have an integer k such that floor(10^k * a(n+1)/a(n)) = 3.

Apparently, n -> a(n)/n has two accumulation points: 2 and 2/3.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1000

Example

The first terms, alongside a(n+1)/a(n), are:
  n   a(n)  a(n+1)/a(n)
  --  ----  -----------
   1     1  3
   2     3  3
   3     9  3
   4    27  0.370370...
   5    10  3
   6    30  0.366666...
   7    11  0.363636...
   8     4  3
   9    12  3
  10    36  0.361111...
  11    13  0.384615...
  12     5  3

Crossrefs

See A328752 for similar sequences.

Sequence in context: A070360 A248131 A070346 * A070345 A272584 A070359

Adjacent sequences: A328751 A328752 A328753 * A328755 A328756 A328757

Keyword

nonn,base

Author

Rémy Sigrist, Oct 27 2019

Status

approved