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.

A342115 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the decimal representations of n and of a(n) are the same.

Original entry on oeis.org

0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 98, 99, 97, 96, 95, 94, 93, 92, 91, 90, 89, 87, 88, 86, 85, 84, 83, 82, 81, 80, 79, 78, 76, 77, 75, 74, 73, 72, 71, 70, 69, 68, 67, 65, 66, 64, 63, 62, 61, 60, 59, 58, 57, 56, 54, 55, 53, 52, 51, 50, 49, 48, 47, 46, 45, 43, 44, 42
Offset: 0

Views

Author

Rémy Sigrist, Feb 28 2021

Keywords

Comments

We ignore leading zeros (hence a(0) = 0).
This sequence is a self-inverse permutation of the nonnegative integers.

Examples

			Consider the set of numbers T with two distinct digits, say u and v, such that u appears once and v appears twice:
- the least elements of T are: 100, 101, 110, 112,
- the greatest elements of T are: 995, 996, 997, 998,
- so a(100) = 998, a(101) = 997, a(110) = 996, a(112) = 995.

Links

Crossrefs

See A342102 for similar sequences.
Cf. A055641, A268643, A316863, A316864, A316865, A316866, A316867, A316868, A316869, A102683.

Programs

  • PARI
    See Links section.

Formula

a(d * (10^k-1)/9) = (10-d) * (10^k-1)/9 for any k >= 0 and d = 1..9.
a(n) < 10^k for any n < 10^k.

A342116 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the factorial base representations of n and of a(n) are the same.

Original entry on oeis.org

0, 1, 5, 3, 4, 2, 21, 18, 17, 9, 23, 16, 15, 22, 20, 12, 11, 8, 7, 19, 14, 6, 13, 10, 105, 93, 90, 96, 117, 114, 63, 81, 72, 33, 113, 65, 112, 111, 108, 64, 107, 60, 104, 103, 102, 57, 119, 100, 48, 99, 98, 97, 59, 95, 94, 92, 91, 45, 89, 52, 41, 88, 87, 30
Offset: 0

Views

Author

Rémy Sigrist, Feb 28 2021

Keywords

Comments

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

Examples

			The first terms, in decimal and in factorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
  n   a(n)  fact(n)  fact(a(n))  freq(n)
  --  ----  -------  ----------  ------------
   0     0        0           0  ()
   1     1        1           1  (1)
   2     5       10          21  (1, 1)
   3     3       11          11  (2)
   4     4       20          20  (1, 1)
   5     2       21          10  (1, 1)
   6    21      100         311  (1, 2)
   7    18      101         300  (1, 2)
   8    17      110         221  (1, 2)
   9     9      111         111  (3)
  10    23      120         321  (1, 1, 1)
  11    16      121         220  (1, 2)
  12    15      200         211  (1, 2)

Links

Crossrefs

See A342102 for similar sequences.
Cf. A007489, A108731.

Programs

  • PARI
    See Links section.

Formula

a(n) < k! for any n < k!.
a(A007489(n)) = A007489(n).

A342117 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the primorial base representations of n and of a(n) are the same.

Original entry on oeis.org

0, 1, 5, 3, 4, 2, 27, 24, 21, 9, 29, 18, 17, 28, 26, 16, 15, 12, 11, 25, 23, 8, 22, 20, 7, 19, 14, 6, 13, 10, 189, 147, 144, 180, 207, 204, 111, 159, 150, 39, 201, 129, 198, 197, 196, 120, 195, 108, 192, 191, 188, 99, 209, 187, 186, 184, 183, 90, 208, 182, 77
Offset: 0

Views

Author

Rémy Sigrist, Feb 28 2021

Keywords

Comments

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

Examples

			The first terms, in decimal and in primorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
  n   a(n)  prim(n)  prim(a(n))  freq(n)
  --  ----  -------  ----------  ------------
   0     0        0           0  ()
   1     1        1           1  (1)
   2     5       10          21  (1, 1)
   3     3       11          11  (2)
   4     4       20          20  (1, 1)
   5     2       21          10  (1, 1)
   6    27      100         411  (1, 2)
   7    24      101         400  (1, 2)
   8    21      110         311  (1, 2)
   9     9      111         111  (3)
  10    29      120         421  (1, 1, 1)
  11    18      121         300  (1, 2)
  12    17      200         221  (1, 2)

Links

Crossrefs

See A342102 for similar sequences.
Cf. A002110, A235168.

Programs

  • PARI
    See Links section.

Formula

a(n) < A002110(k) for any n < A002110(k).
Showing 1-3 of 3 results.

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