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.

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

0,3

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..2309

Rémy Sigrist, Colored scatterplot of the first 2*3*5*7*11*13 terms (where the color is function of the multiset of frequencies of n)

Rémy Sigrist, PARI program for A342117

Index entries for sequences related to primorial base

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) < A002110(k) for any n < A002110(k).

Example

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)

Prog

(PARI) See Links section.

Crossrefs

See A342102 for similar sequences.

Cf. A002110, A235168.

Sequence in context: A222229 A168360 A342116 * A107488 A114236 A178481

Adjacent sequences: A342114 A342115 A342116 * A342118 A342119 A342120

Keyword

nonn,base

Author

Rémy Sigrist, Feb 28 2021

Status

approved