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.

A368230 Inverse permutation to A368229.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 4, 7, 8, 9, 11, 12, 15, 19, 20, 16, 21, 22, 10, 13, 14, 17, 23, 24, 18, 25, 26, 27, 29, 30, 33, 37, 38, 34, 39, 40, 45, 49, 50, 57, 65, 66, 58, 67, 68, 46, 51, 52, 59, 69, 70, 60, 71, 72, 28, 31, 32, 35, 41, 42, 36, 43, 44, 47, 53, 54, 61, 73
Offset: 0

Views

Author

Rémy Sigrist, Dec 18 2023

Keywords

Examples

			A368229(42) = 59, so a(59) = 42.

Links

Crossrefs

Cf. A368229.

Programs

  • PARI
    See Links section.

A368225 Irregular table of nonnegative integers read by rows: the 1's in the binary expansion of n exactly match the nonzero digits in the balanced ternary expansions of the terms in the n-th row.

Original entry on oeis.org

0, 1, 3, 2, 4, 9, 8, 10, 6, 12, 5, 7, 11, 13, 27, 26, 28, 24, 30, 23, 25, 29, 31, 18, 36, 17, 19, 35, 37, 15, 21, 33, 39, 14, 16, 20, 22, 32, 34, 38, 40, 81, 80, 82, 78, 84, 77, 79, 83, 85, 72, 90, 71, 73, 89, 91, 69, 75, 87, 93, 68, 70, 74, 76, 86, 88, 92, 94
Offset: 0

Views

Author

Rémy Sigrist, Dec 18 2023

Keywords

Comments

As a flat sequence, this is a permutation of the nonnegative integers with inverse A368226 and infinitely many fixed points (see Formula section).
Row 0 has one term, and for n > 0, row n has A048896(n-1) terms.
For any n >= 0, row n ends with A005836(n+1).

Examples

			Table T(n, k) begins:
    0;
    1;
    3;
    2, 4;
    9;
    8, 10;
    6, 12;
    5, 7, 11, 13;
    27;
    26, 28;
    24, 30;
    23, 25, 29, 31;
    18, 36;
    17, 19, 35, 37;
    15, 21, 33, 39;
    14, 16, 20, 22, 32, 34, 38, 40;
    81;
    ...

Links

Crossrefs

See A368229 and A368239 for similar sequences.
Cf. A003462, A005836, A048896, A343231, A353662, A368226 (inverse).

Programs

  • PARI
    row(n) = { my (r = [sign(n)], b = binary(n)); for (k = 2, #b, r = [3*v+b[k]|v<-r]; if (b[k], r = concat(r, [v-2|v<-r]););); Set(r); }

Formula

A343231(T(n, k)) = n.
a(m) = m for any m in A003462.

A371257 Irregular triangle T(n, k), n >= 0, k = 1..2^A005811(n), read by rows; the n-th row lists the numbers m such that A371256(m) = n.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 4, 8, 9, 17, 18, 22, 10, 11, 15, 16, 19, 20, 21, 23, 12, 14, 24, 25, 13, 26, 27, 53, 54, 67, 28, 29, 51, 52, 55, 56, 66, 68, 30, 32, 33, 34, 46, 47, 48, 50, 57, 59, 60, 61, 64, 65, 69, 70, 31, 35, 45, 49, 58, 62, 63, 71, 36, 44, 72, 76
Offset: 0

Views

Author

Rémy Sigrist, Mar 16 2024

Keywords

Comments

The n-th row has 2^A005811(n) terms.
As a flat sequence, this is a permutation of the nonnegative integers, with inverse A371258.

Examples

			Triangle T(n, k) begins:
  n   n-th row
  --  --------------------------------------------------------------
   0  0
   1  1, 2
   2  3, 5, 6, 7
   3  4, 8
   4  9, 17, 18, 22
   5  10, 11, 15, 16, 19, 20, 21, 23
   6  12, 14, 24, 25
   7  13, 26
   8  27, 53, 54, 67
   9  28, 29, 51, 52, 55, 56, 66, 68
  10  30, 32, 33, 34, 46, 47, 48, 50, 57, 59, 60, 61, 64, 65, 69, 70
  11  31, 35, 45, 49, 58, 62, 63, 71
  12  36, 44, 72, 76
  13  37, 38, 42, 43, 73, 74, 75, 77
  14  39, 41, 78, 79
  15  40, 80
.
Triangle T(n, k) begins, in ternary, with row indexes in binary:
  bin(n)  n-th row in ternary
  ------  ----------------------------------------------
       0  0
       1  1, 2
      10  10, 12, 20, 21
      11  11, 22
     100  100, 122, 200, 211
     101  101, 102, 120, 121, 201, 202, 210, 212
     110  110, 112, 220, 221
     111  111, 222
    1000  1000, 1222, 2000, 2111
    1001  1001, 1002, 1220, 1221, 2001, 2002, 2110, 2112

Links

Crossrefs

See A371265 for a similar sequence.
Cf. A005811, A166242, A368229, A371256.

Programs

  • PARI
    \\ See Links section.
Showing 1-3 of 3 results.

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