A109681 "Sloping ternary numbers": write numbers in ternary under each other (right-justified), read diagonals in upward direction, convert to decimal.

0, 1, 5, 3, 4, 8, 6, 16, 11, 9, 10, 14, 12, 13, 17, 15, 25, 20, 18, 19, 23, 21, 22, 26, 51, 34, 29, 27, 28, 32, 30, 31, 35, 33, 43, 38, 36, 37, 41, 39, 40, 44, 42, 52, 47, 45, 46, 50, 48, 49, 53, 78, 61, 56, 54, 55, 59, 57, 58, 62, 60, 70, 65, 63, 64, 68, 66

Offset: 0

Author

Philippe Deléham, Aug 08 2005

Keywords

• nonn
• nice
• easy
• base

Comments

All terms are distinct, but certain terms (see A109682) are missing.

For the terms 3^k-1 (all 2's in ternary), the diagonal is not started at the leading 2, but at the leading 1 of the following term. - Georg Fischer, Mar 13 2020

Examples

			number diagonal decimal
    0      0     0
    1      1     1
    2     12     5
   10     10     3
   11     11     4
   12     22     8
   20     20     6
   21    121    16
   22    102    11
  100    100     9
  101    101    10
  102    112    14
  110    110    12
  11.    ...   ...
  1.
  .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Georg Fischer, Perl program

Crossrefs

Cf. A109682 (complement), A109683 (ternary version), A109684.

Cf. A102370 (base 2), A325644 (base 4), A325645 (base 5), A325692 (base 6), A325693 (base 7), A325805 (base 8), A325829 (base 9), A103205 (base 10).

Cf. A030341.

Programs

Haskell

a109681 n = a109681_list !! n
a109681_list = map (foldr (\d v -> 3 * v + d) 0) $ f a030341_tabf where
   f vss = (g 0 vss) : f (tail vss)
   g k (ws:wss) = if k < length ws then ws !! k : g (k + 1) wss else []
-- Reinhard Zumkeller, Nov 19 2013

Maple

t:= (n, i)-> (d-> `if`(i=0, d, t(m, i-1)))(irem(n, 3, 'm')):
b:= (n, i)-> `if`(3^i>n, 0, t(n,i) +3*b(n+1, i+1)):
a:= n-> b(n, 0):
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 13 2020

Perl

Cf. link.

Extensions

Conjectured g.f. and recurrence removed by Georg Fischer, Mar 13 2020