A325829 -id:A325829 - cp's OEIS frontend

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

Philippe Deléham, Aug 08 2005

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

			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.
  .

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

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.

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

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.
```

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

A103205 Write numbers in decimal under each other, then read diagonals in upward direction.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 19, 10, 11, 12, 13, 14, 15, 16, 17, 18, 29, 20, 21, 22, 23, 24, 25, 26, 27, 28, 39, 30, 31, 32, 33, 34, 35, 36, 37, 38, 49, 40, 41, 42, 43, 44, 45, 46, 47, 48, 59, 50, 51, 52, 53, 54, 55, 56, 57, 58, 69, 60, 61, 62, 63, 64, 65, 66, 67, 68, 79, 70, 71, 72, 73, 74, 75, 76, 77, 78, 89, 80, 81, 82, 83, 84, 85, 86, 87, 88

Offset: 0

N. J. A. Sloane, Mar 27 2005

Decimal analog of A102370.

Seiichi Manyama, Table of n, a(n) for n = 0..10000
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp. Preprint versions: [pdf, ps].

Cf. A102370 (base 2), A109681 (base 3), A325644 (base 4), A325645 (base 5), A325692 (base 6), A325693 (base 7), A325805 (base 8), A325829 (base 9), this sequence (base 10).

A325644 "Sloping quaternary numbers": write numbers in quaternary under each other (right-justified), read diagonals in upward direction, convert to decimal.

Original entry on oeis.org

0, 1, 2, 7, 4, 5, 6, 11, 8, 9, 10, 15, 12, 13, 30, 19, 16, 17, 18, 23, 20, 21, 22, 27, 24, 25, 26, 31, 28, 29, 46, 35, 32, 33, 34, 39, 36, 37, 38, 43, 40, 41, 42, 47, 44, 45, 62, 51, 48, 49, 50, 55, 52, 53, 54, 59, 56, 57, 58, 63, 60, 125, 78, 67, 64, 65, 66, 71, 68, 69, 70

Offset: 0

Seiichi Manyama, Sep 07 2019

			    0
    1
    2
    3
   10
   11
   12
   13
   20
   21
   22
   23
   30
   31
   32
   33
  100
...
The upward-sloping diagonals are:
0
1
2
13
10
11
12
23
20
21
22
33
30
31
132
103
100
...
giving 0, 1, 2, "7", 4, 5, 6, "11", 8, 9, 10, "15", 12, 13, "30", "19", 16, ...

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Quaternary numeral system

Cf. A102370 (base 2), A109681 (base3), this sequence (base 4), A325645 (base 5), A325692 (base 6), A325693 (base 7), A325805 (base 8), A325829 (base 9), A103205 (base 10).

def A(m, n)
  ary = [0]
  n.times{|i|
    (m ** i - i..m ** (i + 1) - i - 2).each{|j|
      ary << (0..i).inject(0){|s, k| s + (j + k).to_s(m)[-1 - k].to_i * m ** k}
    }
  }
  ary
end
p A(4, 4)

A325645 "Sloping quinary numbers": write numbers in quinary under each other (right-justified), read diagonals in upward direction, convert to decimal.

Original entry on oeis.org

0, 1, 2, 3, 9, 5, 6, 7, 8, 14, 10, 11, 12, 13, 19, 15, 16, 17, 18, 24, 20, 21, 22, 48, 29, 25, 26, 27, 28, 34, 30, 31, 32, 33, 39, 35, 36, 37, 38, 44, 40, 41, 42, 43, 49, 45, 46, 47, 73, 54, 50, 51, 52, 53, 59, 55, 56, 57, 58, 64, 60, 61, 62, 63, 69, 65, 66, 67, 68, 74, 70, 71

Offset: 0

Seiichi Manyama, Sep 07 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Quinary

Cf. A102370 (base 2), A109681 (base3), A325644 (base 4), this sequence (base 5), A325692 (base 6), A325693 (base 7), A325805 (base 8), A325829 (base 9), A103205 (base 10).

def A(m, n)
  ary = [0]
  n.times{|i|
    (m ** i - i..m ** (i + 1) - i - 2).each{|j|
      ary << (0..i).inject(0){|s, k| s + (j + k).to_s(m)[-1 - k].to_i * m ** k}
    }
  }
  ary
end
p A(5, 3)

A325692 "Sloping senary numbers": write numbers in senary (that is, base 6) under each other (right-justified), read diagonals in upward direction, convert to decimal.

Original entry on oeis.org

0, 1, 2, 3, 4, 11, 6, 7, 8, 9, 10, 17, 12, 13, 14, 15, 16, 23, 18, 19, 20, 21, 22, 29, 24, 25, 26, 27, 28, 35, 30, 31, 32, 33, 70, 41, 36, 37, 38, 39, 40, 47, 42, 43, 44, 45, 46, 53, 48, 49, 50, 51, 52, 59, 54, 55, 56, 57, 58, 65, 60, 61, 62, 63, 64, 71, 66, 67, 68, 69, 106, 77, 72

Offset: 0

Seiichi Manyama, Sep 07 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Senary

Cf. A102370 (base 2), A109681 (base 3), A325644 (base 4), A325645 (base 5), this sequence (base 6), A325693 (base 7), A325805 (base 8), A325829 (base 9), A103205 (base 10).

A325693 "Sloping septenary numbers": write numbers in septenary under each other (right-justified), read diagonals in upward direction, convert to decimal.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 13, 7, 8, 9, 10, 11, 12, 20, 14, 15, 16, 17, 18, 19, 27, 21, 22, 23, 24, 25, 26, 34, 28, 29, 30, 31, 32, 33, 41, 35, 36, 37, 38, 39, 40, 48, 42, 43, 44, 45, 46, 96, 55, 49, 50, 51, 52, 53, 54, 62, 56, 57, 58, 59, 60, 61, 69, 63, 64, 65, 66, 67, 68, 76, 70, 71

Offset: 0

Seiichi Manyama, Sep 07 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A102370 (base 2), A109681 (base 3), A325644 (base 4), A325645 (base 5), A325692 (base 6), this sequence (base 7), A325805 (base 8), A325829 (base 9), A103205 (base 10).

A325805 "Sloping octal numbers": write numbers in octal under each other (right-justified), read diagonals in upward direction, convert to decimal.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 15, 8, 9, 10, 11, 12, 13, 14, 23, 16, 17, 18, 19, 20, 21, 22, 31, 24, 25, 26, 27, 28, 29, 30, 39, 32, 33, 34, 35, 36, 37, 38, 47, 40, 41, 42, 43, 44, 45, 46, 55, 48, 49, 50, 51, 52, 53, 54, 63, 56, 57, 58, 59, 60, 61, 126, 71, 64, 65, 66, 67, 68, 69, 70, 79

Offset: 0

Seiichi Manyama, Sep 07 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Octal

Cf. A102370 (base 2), A109681 (base 3), A325644 (base 4), A325645 (base 5), A325692 (base 6), A325693 (base 7), this sequence (base 8), A325829 (base 9), A103205 (base 10).

cp's OEIS Frontend

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

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Haskell

Maple

Perl

Extensions

A103205 Write numbers in decimal under each other, then read diagonals in upward direction.

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A325644 "Sloping quaternary numbers": write numbers in quaternary under each other (right-justified), read diagonals in upward direction, convert to decimal.

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Ruby

A325645 "Sloping quinary numbers": write numbers in quinary under each other (right-justified), read diagonals in upward direction, convert to decimal.

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Programs

Ruby

A325692 "Sloping senary numbers": write numbers in senary (that is, base 6) under each other (right-justified), read diagonals in upward direction, convert to decimal.

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Crossrefs

A325693 "Sloping septenary numbers": write numbers in septenary under each other (right-justified), read diagonals in upward direction, convert to decimal.

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Author

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Links

Crossrefs

A325805 "Sloping octal numbers": write numbers in octal under each other (right-justified), read diagonals in upward direction, convert to decimal.

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Author

Keywords

Links

Crossrefs