A331275 -id:A331275 - cp's OEIS frontend

A331274 a(n) is the greatest binary anagram of n not yet in the sequence.

1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 14, 9, 13, 11, 15, 16, 24, 20, 28, 18, 26, 25, 30, 17, 22, 21, 29, 19, 27, 23, 31, 32, 48, 40, 56, 36, 52, 50, 60, 34, 49, 44, 58, 42, 57, 54, 62, 33, 41, 38, 53, 37, 51, 46, 61, 35, 45, 43, 59, 39, 55, 47, 63, 64, 96, 80, 112

Offset: 1

Rémy Sigrist, Jan 13 2020

Leading zeros are ignored.

This sequence is a self-inverse permutation of the natural numbers.

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   1     1       1          1
   2     2      10         10
   3     3      11         11
   4     4     100        100
   5     6     101        110
   6     5     110        101
   7     7     111        111
   8     8    1000       1000
   9    12    1001       1100
  10    10    1010       1010
  11    14    1011       1110
  12     9    1100       1001
  13    13    1101       1101
  14    11    1110       1011
  15    15    1111       1111

Rémy Sigrist, Table of n, a(n) for n = 1..8192
Rémy Sigrist, Colored scatterplot of the first 2^13 terms (where the color is function of the Hamming weight of n)
Rémy Sigrist, PARI program for A331274
Index entries for sequences that are permutations of the natural numbers

Cf. A007318, A187769, A298847, A331275 (ternary analog).

PARI
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a(A187769(n, k)) = A187769(n, A007318(n-1)+1-k) for any n > 0 and k = 1..A007318(n-1).

A352760 Lexigraphically earliest sequence of distinct nonnegative integers such that for any n >= 0, among the ternary digits of n and a(n) (counted with multiplicity) there are as many 1's as 2's.

Original entry on oeis.org

0, 2, 1, 6, 8, 5, 3, 7, 4, 17, 20, 11, 24, 26, 18, 15, 23, 9, 14, 19, 10, 21, 25, 16, 12, 22, 13, 35, 53, 29, 56, 62, 47, 33, 51, 27, 60, 74, 54, 78, 80, 71, 59, 72, 44, 45, 61, 32, 65, 77, 50, 34, 52, 28, 38, 55, 30, 57, 69, 42, 36, 46, 31, 63, 73, 48, 75, 79

Offset: 0

Rémy Sigrist, Jul 05 2022

This sequence is a self-inverse permutation of the nonnegative integers.

			The first terms, alongside their ternary expansions, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     2       1          2
   2     1       2          1
   3     6      10         20
   4     8      11         22
   5     5      12         12
   6     3      20         10
   7     7      21         21
   8     4      22         11
   9    17     100        122
  10    20     101        202
  11    11     102        102
  12    24     110        220

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

Cf. A004488, A039001 (fixed points), A331275, A355504.

PARI
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a(n) = n iff n belongs to A039001.

a(n) < 3^k iff n < 3^k.

A337305 a(n) is the greatest number m not yet in the sequence such that the ternary expansions of n and of m have the same runs of consecutive equal digits (up to order but with multiplicity).

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 21, 12, 13, 22, 19, 16, 25, 18, 15, 20, 11, 14, 23, 24, 17, 26, 27, 28, 63, 30, 37, 64, 57, 48, 75, 36, 31, 66, 39, 40, 67, 58, 49, 76, 55, 46, 69, 34, 43, 70, 73, 52, 79, 54, 45, 56, 33, 42, 65, 60, 61, 74, 29, 32, 59, 38, 41

Offset: 0

Rémy Sigrist, Aug 22 2020

This sequence is the base 3 analog of A337304.

This sequence is a self-inverse permutation of the nonnegative integers.

			For n = 144:
- the ternary representation of 144 is "12100",
- the corresponding runs of consecutive equal digits are: "1", "2", "1", "00",
- there are five numbers k with the same multiset of runs:
    k    ter(k)
    ---  -------
     86  "10012"
     88  "10021"
    136  "12001"
    144  "12100"
    190  "21001"
- so a(86) = 190,
     a(88) = 144,
     a(136) = 136,
     a(144) = 88,
     a(190) = 86.

Rémy Sigrist, Table of n, a(n) for n = 0..6561
Rémy Sigrist, PARI program for A337305
Index entries for sequences that are permutations of the natural numbers

Cf. A331275, A337304.

PARI
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See Links section.
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cp's OEIS Frontend

A331274 a(n) is the greatest binary anagram of n not yet in the sequence.

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A352760 Lexigraphically earliest sequence of distinct nonnegative integers such that for any n >= 0, among the ternary digits of n and a(n) (counted with multiplicity) there are as many 1's as 2's.

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Formula

A337305 a(n) is the greatest number m not yet in the sequence such that the ternary expansions of n and of m have the same runs of consecutive equal digits (up to order but with multiplicity).

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI