A319023 Let S be the sequence generated by these rules: 1 is in S, and if k is in S, then A057168(k) and A319021(k) are in S, and duplicates are deleted as they occur; a(n) is the n-th term of S.

1, 2, 3, 4, 5, 9, 8, 6, 7, 10, 27, 16, 14, 11, 12, 29, 81, 32, 20, 19, 13, 17, 18, 30, 31, 82, 243, 64, 34, 24, 22, 21, 15, 23, 28, 39, 36, 47, 33, 84, 245, 729, 128, 66, 38, 25, 35, 43, 45, 40, 54, 55, 49, 37, 88, 90, 246, 247, 730, 2187, 256, 130, 68, 72, 41

Offset: 1

Author

Rémy Sigrist, Sep 08 2018

Keywords

• nonn
• base
• look

Comments

This sequence is a permutation of the natural numbers (with inverse A319024):

- this sequence is injective,

- this sequence is surjective: by contradiction:

- let m be the least integer missing from the sequence,

- as a(1) = 1, we have m > 1,

- also, m belongs to A000225 and to A062318,

- however the only positive integer belonging to both sequences is 1,

- hence a contradiction, QED.

Examples

			The first terms, alongside b(n) = A057168(a(n)) and t(n) = A319021(a(n)), are:
  n   a(n)  b(n)  t(n)
  --  ----  ----  ----
   1     1     2     3
   2     2     4     4
   3     3     5     9
   4     4     8     6
   5     5     6     7
   6     9    10    27
   7     8    16    14
   8     6     9    10
   9     7    11    11
  10    10    12    12
  11    27    29    81
  12    16    32    20
  13    14    19    16
  14    11    13    13
  15    12    17    18
  16    29    30    31
  17    81    82   243
  18    32    64    34
  19    20    24    22
  20    19    21    21
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A319023
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000225, A057168, A062318, A319021, A319024 (inverse).

Programs

PARI

See Links section.