A360959 -id:A360959 - cp's OEIS frontend

A360960 Inverse permutation to A360959.

0, 1, 3, 2, 7, 4, 6, 5, 15, 8, 14, 9, 13, 10, 12, 11, 31, 23, 30, 24, 29, 25, 28, 26, 27, 21, 22, 16, 20, 17, 19, 18, 35, 32, 34, 33, 63, 51, 62, 52, 61, 53, 60, 54, 59, 55, 58, 56, 57, 36, 50, 37, 49, 38, 48, 39, 47, 40, 46, 41, 45, 42, 44, 43, 127, 111, 126

Offset: 0

Rémy Sigrist, Feb 27 2023

			A360959(42) = 61, so a(61) = 42.

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A360959.

PARI
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See Links section.
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a(n) < 2^k for any n < 2^k.

A360982 Order the nonnegative integers by increasing binary length of values, then by decreasing binary length of values squared, then by increasing binary length of values cubed, etc.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 5, 4, 12, 15, 14, 13, 10, 9, 8, 11, 23, 24, 25, 27, 30, 31, 29, 28, 26, 20, 18, 17, 16, 19, 21, 22, 46, 47, 48, 50, 49, 54, 55, 59, 60, 61, 63, 62, 58, 56, 57, 52, 51, 53, 39, 40, 36, 35, 34, 32, 33, 37, 38, 42, 41, 43, 44, 45, 91, 92, 93, 94

Offset: 0

Rémy Sigrist, Feb 27 2023

We ignore leading zeros (and 0 is assumed to have binary length 0).
This sequence is a permutation of the nonnegative integers with inverse A360983.
The order of appearance of two distinct integers, say x and y with x > y, depends on the parity of A360963(x, y): even implies x appears before y, odd implies x appears after y.

			The first terms, alongside the binary length of their first powers, are:
  n   a(n)  w1  w2  w3  w4  w5  w6
  --  ----  --  --  --  --  --  --
   0     0   0
   1     1   1
   2     3   2   4
   3     2   2   3
   4     6   3   6   8
   5     7   3   6   9
   6     5   3   5   7  10
   7     4   3   5   7   9
   8    12   4   8  11
   9    15   4   8  12  16  20  24
  10    14   4   8  12  16  20  23
  11    13   4   8  12  15
  12    10   4   7  10  14
  13     9   4   7  10  13  16  20
  14     8   4   7  10  13  16  19
  15    11   4   7  11

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, Scatterplot of the first 2^15 terms
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A360959 for a similar sequence.

Cf. A360963, A360983 (inverse).

PARI
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See Links section.
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cp's OEIS Frontend

A360960 Inverse permutation to A360959.

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