A375112 -id:A375112 - cp's OEIS frontend

A375113 Inverse permutation to A375112.

1, 3, 2, 6, 4, 10, 5, 14, 8, 7, 15, 11, 21, 9, 20, 12, 27, 13, 34, 18, 16, 28, 17, 35, 23, 22, 36, 29, 45, 19, 43, 24, 44, 30, 54, 25, 53, 31, 64, 26, 63, 32, 75, 33, 87, 41, 37, 55, 38, 65, 39, 76, 40, 88, 49, 46, 66, 47, 77, 48, 89, 58, 56, 78, 57, 90, 68

Offset: 1

Rémy Sigrist, Jul 30 2024

nonn

			A375112(42) = 72, so a(72) = 42.

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

Cf. A375112.

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A375110 Lexicographically earliest sequence of positive integers such that the pairs (a(n) mod a(n+1), a(n+1)) are all distinct.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 4, 3, 5, 4, 4, 5, 5, 6, 4, 6, 5, 7, 5, 8, 6, 6, 7, 6, 8, 7, 7, 8, 8, 9, 6, 9, 7, 9, 8, 10, 7, 10, 8, 11, 7, 11, 8, 12, 8, 13, 9, 9, 10, 9, 11, 9, 12, 9, 13, 10, 10, 11, 10, 12, 10, 13, 11, 11, 12, 11, 13, 12, 12, 13, 13, 14, 9, 14, 10, 14, 11

Offset: 1

Rémy Sigrist, Jul 30 2024

nonn

The value 1 appears twice; for any v > 1, v appears v times.

This sequence shares graphical features with A335943.

			The first terms, alongside the corresponding pairs, are:
  n   a(n)  (a(n) mod a(n+1), a(n+1))
  --  ----  -------------------------
   1     1  (0, 1)
   2     1  (1, 2)
   3     2  (0, 2)
   4     2  (2, 3)
   5     3  (0, 3)
   6     3  (3, 4)
   7     4  (1, 3)
   8     3  (3, 5)
   9     5  (1, 4)
  10     4  (0, 4)
  11     4  (4, 5)
  12     5  (0, 5)
  13     5  (5, 6)
  14     6  (2, 4)
  15     4  (4, 6)

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

See A375114 and A375115 for similar sequences.

Cf. A335943, A375111, A375112.

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cp's OEIS Frontend

A375113 Inverse permutation to A375112.

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