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

0,3

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Georg Fischer, Perl program

Example

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.
  .

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

Prog

(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
(Perl) Cf. link.

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.

Sequence in context: A193090 A004162 A319053 * A196406 A070367 A086308

Adjacent sequences: A109678 A109679 A109680 * A109682 A109683 A109684

Keyword

nonn,nice,easy,base

Author

Philippe Deléham, Aug 08 2005

Extensions

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

Status

approved