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

1,2

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.

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A092975 A164340 A046021 * A335910 A362814 A371152

Adjacent sequences: A319020 A319021 A319022 * A319024 A319025 A319026

Keyword

nonn,base,look

Author

Rémy Sigrist, Sep 08 2018

Status

approved