A370631 -id:A370631 - cp's OEIS frontend

A370632 Inverse permutation to A370631.

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

Offset: 1

Rémy Sigrist, May 01 2024

			A370631(4) = 11, so a(11) = 4.

Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A370631.

PARI
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A370630 Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have exactly one common term.

Original entry on oeis.org

1, 4, 3, 11, 8, 9, 6, 5, 7, 2, 10, 12, 14, 13, 15, 16, 18, 17, 20, 23, 21, 22, 19, 25, 26, 24, 27, 29, 28, 30, 35, 33, 37, 32, 38, 34, 36, 31, 41, 42, 39, 43, 47, 40, 44, 48, 45, 49, 46, 52, 60, 53, 56, 51, 58, 50, 59, 55, 57, 54, 61, 63, 62, 64, 68, 65, 69

Offset: 1

Rémy Sigrist, May 01 2024

Conjecture: this sequence is a permutation of the positive integers.

			The first terms, alongside the Zeckendorf expansion in binary of a(n), are:
  n   a(n)  z(a(n))
  --  ----  -------
   1     1        1
   2     4      101
   3     3      100
   4    11    10100
   5     8    10000
   6     9    10001
   7     6     1001
   8     5     1000
   9     7     1010
  10     2       10
  11    10    10010
  12    12    10101

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
Index entries for sequences related to Zeckendorf expansion of n

Cf. A000120, A003714, A226077, A332565, A370631.

PARI
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A000120(A003714(a(n)), A003714(a(n+1))) = 1.

cp's OEIS Frontend

A370632 Inverse permutation to A370631.

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