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

Author

Rémy Sigrist, Feb 28 2021

Keywords

• nonn
• base

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

• 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

Crossrefs

See A342102 for similar sequences.

Cf. A002110, A235168.

Programs

PARI

See Links section.

Formula

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