A348354 The base-5 expansion of a(n) is obtained by replacing 1's, 2's, 3's and 4's by 3's, 4's, 1's and 2's, respectively, in the base-5 expansion of n.

0, 3, 4, 1, 2, 15, 18, 19, 16, 17, 20, 23, 24, 21, 22, 5, 8, 9, 6, 7, 10, 13, 14, 11, 12, 75, 78, 79, 76, 77, 90, 93, 94, 91, 92, 95, 98, 99, 96, 97, 80, 83, 84, 81, 82, 85, 88, 89, 86, 87, 100, 103, 104, 101, 102, 115, 118, 119, 116, 117, 120, 123, 124, 121

Offset

0,2

Comments

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

It is possible to build a similar sequence for any fixed base b > 1 and any permutation p of {1, ..., b-1}.

This sequence is interesting as it satisfies f(a(n)) = -f(n), where f(n) = (A316657(n), A316658(n)).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..3124

Index entries for sequences that are permutations of the natural numbers

Formula

A316657(n) + A316657(a(n)) = 0.

A316658(n) + A316658(a(n)) = 0.

Example

The first terms, in decimal and in base 5, are:
  n   a(n)  q(n)  q(a(n))
  --  ----  ----  -------
   0     0     0        0
   1     3     1        3
   2     4     2        4
   3     1     3        1
   4     2     4        2
   5    15    10       30
   6    18    11       33
   7    19    12       34
   8    16    13       31
   9    17    14       32
  10    20    20       40

Mathematica

a[n_] := With[{d = {0, 3, 4, 1, 2}}, FromDigits[d[[IntegerDigits[n, 5] + 1]], 5]]; Array[a, 64, 0] (* Amiram Eldar, Oct 16 2021 *)

Prog

(PARI) a(n, p=[3, 4, 1, 2]) = fromdigits(apply(d -> if (d, p[d], 0), digits(n, #p+1)), #p+1)

Crossrefs

See A004488, A048647 and A348355 for similar sequences.

Cf. A316657, A316658.

Sequence in context: A171073 A021297 A124909 * A356708 A281098 A090279

Adjacent sequences: A348351 A348352 A348353 * A348355 A348356 A348357

Keyword

nonn,base,easy

Author

Rémy Sigrist, Oct 14 2021

Status

approved