A371265 -id:A371265 - cp's OEIS frontend

A371266 Inverse permutation to A371265.

0, 1, 2, 3, 4, 5, 7, 8, 9, 6, 10, 11, 12, 13, 14, 16, 17, 20, 28, 21, 22, 23, 29, 30, 24, 25, 18, 15, 19, 26, 27, 31, 32, 34, 35, 36, 33, 37, 38, 39, 40, 41, 43, 44, 47, 55, 48, 49, 50, 56, 59, 67, 68, 83, 91, 84, 69, 70, 60, 61, 71, 72, 73, 62, 74, 85, 86, 92

Offset: 0

Rémy Sigrist, Mar 16 2024

			A371265(42) = 81, so a(81) = 42.

Rémy Sigrist, Table of n, a(n) for n = 0..9841
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A371265.

PARI
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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

Rémy Sigrist, Mar 16 2024

The n-th row has 2^A005811(n) terms.

As a flat sequence, this is a permutation of the nonnegative integers, with inverse A371258.

			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

Rémy Sigrist, Table of n, a(n) for n = 0..6560
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A371265 for a similar sequence.

Cf. A005811, A166242, A368229, A371256.

PARI
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A371263 The run lengths transform of the balanced ternary expansion of n corresponds to the run lengths transform of the binary expansion of a(n).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, Mar 16 2024

For any v > 0, the value v appears A225081(v-1) times in the sequence.

			The first terms, alongside the balanced ternary expansion of n and the binary expansion of a(n), are:
  n   a(n)  bter(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     5      1T0        101
   7     5      1T1        101
   8     5      10T        101
   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     9     1TT0       1001

Rémy Sigrist, Table of n, a(n) for n = 0..9841

See A371256 for a similar sequence.

Cf. A225081, A371265.

a(n) = { my (r = [], d, l, v = 0); while (n, d = centerlift(Mod(n, 3)); l = 0; while (centerlift(Mod(n, 3))==d, n = (n-d)/3; l++;); r = concat(l, r);); for (k = 1, #r, v = (v+k%2)*2^r[k]-k%2); v }

abs(a(n+1) - a(n)) <= 1.

cp's OEIS Frontend

A371266 Inverse permutation to A371265.

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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.

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A371263 The run lengths transform of the balanced ternary expansion of n corresponds to the run lengths transform of the binary expansion of a(n).

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