cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A343228 A binary encoding of the digits "+1" in balanced ternary representation of n.

Original entry on oeis.org

0, 1, 2, 2, 3, 4, 4, 5, 4, 4, 5, 6, 6, 7, 8, 8, 9, 8, 8, 9, 10, 10, 11, 8, 8, 9, 8, 8, 9, 10, 10, 11, 12, 12, 13, 12, 12, 13, 14, 14, 15, 16, 16, 17, 16, 16, 17, 18, 18, 19, 16, 16, 17, 16, 16, 17, 18, 18, 19, 20, 20, 21, 20, 20, 21, 22, 22, 23, 16, 16, 17, 16
Offset: 0

Views

Author

Rémy Sigrist, Apr 08 2021

Keywords

Comments

The ones in the binary representation of a(n) correspond to the digits "+1" in the balanced ternary representation of n.
We can extend this sequence to negative indices: a(-n) = A343229(n) for any n >= 0.

Examples

			The first terms, alongside the balanced ternary representation of n (with "T" instead of digits "-1") and the binary representation of a(n), are:
  n   a(n)  ter(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2      1T         10
   3     2      10         10
   4     3      11         11
   5     4     1TT        100
   6     4     1T0        100
   7     5     1T1        101
   8     4     10T        100
   9     4     100        100
  10     5     101        101
  11     6     11T        110
  12     6     110        110
  13     7     111        111
  14     8    1TTT       1000
  15     8    1TT0       1000

Links

Crossrefs

Cf. A059095, A060372, A140267, A289813, A289831, A343229, A343230, A343231.

Programs

  • PARI
    a(n) = { my (v=0, b=1, t); while (n, t=centerlift(Mod(n, 3)); if (t==+1, v+=b); n=(n-t)\3; b*=2); v }

Formula

a(n) = A289831(A060372(n)).

A343231 A binary encoding of the nonzero digits in balanced ternary representation of n.

Original entry on oeis.org

0, 1, 3, 2, 3, 7, 6, 7, 5, 4, 5, 7, 6, 7, 15, 14, 15, 13, 12, 13, 15, 14, 15, 11, 10, 11, 9, 8, 9, 11, 10, 11, 15, 14, 15, 13, 12, 13, 15, 14, 15, 31, 30, 31, 29, 28, 29, 31, 30, 31, 27, 26, 27, 25, 24, 25, 27, 26, 27, 31, 30, 31, 29, 28, 29, 31, 30, 31, 23
Offset: 0

Views

Author

Rémy Sigrist, Apr 08 2021

Keywords

Comments

The ones in the binary representation of a(n) correspond to the nonzero digits in the balanced ternary representation of n.
We can extend this sequence to negative indices: a(-n) = a(n) for any n >= 0.

Examples

			The first terms, alongside the balanced ternary representation of n (with "T" instead of digits "-1") and the binary representation of a(n), are:
  n   a(n)  ter(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     3      1T         11
   3     2      10         10
   4     3      11         11
   5     7     1TT        111
   6     6     1T0        110
   7     7     1T1        111
   8     5     10T        101
   9     4     100        100
  10     5     101        101
  11     7     11T        111
  12     6     110        110
  13     7     111        111
  14    15    1TTT       1111
  15    14    1TT0       1110

Links

Crossrefs

Cf. A059095, A140267, A289831, A343228, A343229, A343230.

Programs

  • PARI
    a(n) = { my (v=0, b=1, t); while (n, t=centerlift(Mod(n, 3)); if (t, v+=b); n=(n-t)\3; b*=2); v }

Formula

a(n) = A343228(n) + A343229(n).

A343229 A binary encoding of the digits "-1" in balanced ternary representation of n.

Original entry on oeis.org

0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 7, 6, 6, 5, 4, 4, 5, 4, 4, 3, 2, 2, 1, 0, 0, 1, 0, 0, 3, 2, 2, 1, 0, 0, 1, 0, 0, 15, 14, 14, 13, 12, 12, 13, 12, 12, 11, 10, 10, 9, 8, 8, 9, 8, 8, 11, 10, 10, 9, 8, 8, 9, 8, 8, 7, 6, 6, 5, 4, 4, 5, 4, 4, 3, 2, 2, 1, 0
Offset: 0

Views

Author

Rémy Sigrist, Apr 08 2021

Keywords

Comments

The ones in the binary representation of a(n) correspond to the digits "-1" in the balanced ternary representation of n.
We can extend this sequence to negative indices: a(-n) = A343228(n) for any n >= 0.

Examples

			The first terms, alongside the balanced ternary representation of n (with "T" instead of digits "-1") and the binary representation of a(n), are:
  n   a(n)  ter(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     0       1          0
   2     1      1T          1
   3     0      10          0
   4     0      11          0
   5     3     1TT         11
   6     2     1T0         10
   7     2     1T1         10
   8     1     10T          1
   9     0     100          0
  10     0     101          0
  11     1     11T          1
  12     0     110          0
  13     0     111          0
  14     7    1TTT        111
  15     6    1TT0        110

Links

Crossrefs

Cf. A059095, A060373, A140267, A289814, A289831, A343228, A343230, A343231, A005836 (indices of 0's).

Programs

  • PARI
    a(n) = { my (v=0, b=1, t); while (n, t=centerlift(Mod(n, 3)); if (t==-1, v+=b); n=(n-t)\3; b*=2); v }

Formula

a(n) = A289831(A060373(n)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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