A361945 -id:A361945 - cp's OEIS frontend

A361946 If the base-4 expansion of n starts with the digit 1, then replace 2's by 3's and vice versa; if it starts with the digit 2, then replace 1's by 3's and vice versa; if it starts with the digit 3, then replace 1's by 2's and vice versa; a(0) = 0.

0, 1, 2, 3, 4, 5, 7, 6, 8, 11, 10, 9, 12, 14, 13, 15, 16, 17, 19, 18, 20, 21, 23, 22, 28, 29, 31, 30, 24, 25, 27, 26, 32, 35, 34, 33, 44, 47, 46, 45, 40, 43, 42, 41, 36, 39, 38, 37, 48, 50, 49, 51, 56, 58, 57, 59, 52, 54, 53, 55, 60, 62, 61, 63, 64, 65, 67, 66

Offset: 0

Rémy Sigrist, Apr 01 2023

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

			For n = 539:
- the base-4 expansion of 539 is "20123",
- it starts with the digit 2, so we replace 1's by 3's and vice versa,
- so the base-4 expansion of a(539) is "20321", and a(539) = 569.

Cf. A000695, A048647, A057300, A122587, A163241, A361945, A361947.

a(n) = { my (q = digits(n, 4), m = if (#q, [ [0,1,3,2], [0,3,2,1], [0,2,1,3] ][q[1]], [0,1,2,3])); fromdigits(apply (d -> m[1+d], q), 4); }

a(n) = A163241(n) when A122587(n) = 1.
a(n) = A048647(n) when A122587(n) = 2.
a(n) = A057300(n) when A122587(n) = 3.
a(n) = n iff n = d * A000695(k) for some d in {1, 2, 3} and some k >= 0.

A361947 If the rightmost nonzero digit in the base-4 expansion of n is the digit 1, then replace 2's by 3's and vice versa; if it is the digit 2, then replace 1's by 3's and vice versa; if it is the digit 3, then replace 1's by 2's and vice versa; a(0) = 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 14, 11, 8, 13, 10, 7, 12, 9, 6, 15, 16, 17, 50, 35, 20, 21, 62, 43, 56, 29, 58, 39, 44, 25, 54, 47, 32, 49, 34, 19, 52, 53, 46, 27, 40, 61, 42, 23, 28, 57, 38, 31, 48, 33, 18, 51, 36, 37, 30, 59, 24, 45, 26, 55, 60, 41, 22, 63, 64, 65, 194

Offset: 0

Rémy Sigrist, Apr 01 2023

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

			For n = 539:
- the base-4 expansion of 539 is "20123",
- the rightmost nonzero digit is 3, so we replace 1's by 2's and vice versa,
- so the base-4 expansion of a(539) is "10213", and a(539) = 295.

Cf. A000695, A048647, A057300, A065882, A163241, A361945, A361946.

a(n) = { my (m = if (n, [ [0,1,3,2], [0,3,2,1], [0,2,1,3] ][(n / 4^valuation(n, 4)) % 4], [0,1,2,3])); fromdigits(apply (d -> m[1+d], digits(n, 4)), 4); }

a(n) = A163241(n) when A065882(n) = 1.
a(n) = A048647(n) when A065882(n) = 2.
a(n) = A057300(n) when A065882(n) = 3.
a(n) = n iff n = d * A000695(k) for some d in {1, 2, 3} and some k >= 0.

A371268 If the ternary expansion of n starts with a 1, replace 1's by 2's, 2's by 0's, 0's by 1's, if it starts with a 2, replace 2's by 1's, 1's by 0's, 0's by 2's.

Original entry on oeis.org

0, 2, 1, 7, 8, 6, 5, 3, 4, 22, 23, 21, 25, 26, 24, 19, 20, 18, 17, 15, 16, 11, 9, 10, 14, 12, 13, 67, 68, 66, 70, 71, 69, 64, 65, 63, 76, 77, 75, 79, 80, 78, 73, 74, 72, 58, 59, 57, 61, 62, 60, 55, 56, 54, 53, 51, 52, 47, 45, 46, 50, 48, 49, 35, 33, 34, 29, 27

Offset: 0

Rémy Sigrist, Mar 16 2024

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

			The first terms, in decimal and in base 3, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     2       1          2
   2     1       2          1
   3     7      10         21
   4     8      11         22
   5     6      12         20
   6     5      20         12
   7     3      21         10
   8     4      22         11
   9    22     100        211
  10    23     101        212
  11    21     102        210
  12    25     110        221
  13    26     111        222
  14    24     112        220
  15    19     120        201

See A004488 and A361945 for similar sequences.

Cf. A338246, A371256.

a(n) = { my (d = digits(n, 3)); if (#d, d = if (d[1]==1, apply(v -> [1, 2, 0][1+v], d), apply(v -> [2, 0, 1][1+v], d));); fromdigits(d, 3); }

A371256(a(n)) = A371256(n).

cp's OEIS Frontend

A361946 If the base-4 expansion of n starts with the digit 1, then replace 2's by 3's and vice versa; if it starts with the digit 2, then replace 1's by 3's and vice versa; if it starts with the digit 3, then replace 1's by 2's and vice versa; a(0) = 0.

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A361947 If the rightmost nonzero digit in the base-4 expansion of n is the digit 1, then replace 2's by 3's and vice versa; if it is the digit 2, then replace 1's by 3's and vice versa; if it is the digit 3, then replace 1's by 2's and vice versa; a(0) = 0.

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A371268 If the ternary expansion of n starts with a 1, replace 1's by 2's, 2's by 0's, 0's by 1's, if it starts with a 2, replace 2's by 1's, 1's by 0's, 0's by 2's.

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