A359737 Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = A296239(a(n)) has the same sequence of digits, where A296239 gives the distance from the nearest Fibonacci number, cf. A000045.

0, 12, 10, 4, 1, 17, 6, 7, 41, 27, 48, 25, 9, 11, 62, 30, 42, 15, 26, 43, 14, 20, 28, 19, 16, 2, 38, 23, 22, 29, 32, 40, 51, 18, 33, 59, 36, 3, 53, 47, 35, 46, 54, 49, 57, 24, 63, 87, 31, 91, 111, 64, 37, 113, 5, 39, 56, 88, 81, 52, 58, 50, 80, 86, 61, 92, 60, 141, 85, 82, 147

Offset

0,2

Comments

In the definition, "has the same sequence of digits" means that the concatenation of the terms yields the same string of digits, for the sequence a(.) and the sequence d(.).

Conjectured to be a permutation of the nonnegative integers. The inverse permutation would start (0, 4, 25, 37, 3, 54, 6, 7, 104, 12, 2, 13, 1, 106, 20, ...).

Links

Table of n, a(n) for n=0..70.

Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023.

Eric Angelini, Digit-spines, personal blog "Cinquante signes" on blogspot.com, Jan. 11, 2023. [Cached copy]

Example

Below, row "F" lists the closest Fibonacci number to a(n) and row "d" the absolute difference |a(n) - F|. We have the same sequence of digits in rows a (this sequence) and d:
  n :  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14 ...
  a :  0  12  10   4   1  17   6   7  41  27  48  25   9  11  62 ...
  F :  0  13   8   3   1  13   5   8  34  21  55  21   8  13  55 ...
  d :  0   1   2   1   0   4   1   1   7   6   7   4   1   2   7 ...

Prog

(PARI) spine(fibonacci, 200) \\ \\ See A359734 for spine()

Crossrefs

Cf. A296239 (distance from the nearest Fibonacci number), A000045 (the Fibonacci numbers).

Cf. A359734, A359736 (similar for primes and squares).

Sequence in context: A068614 A163920 A038335 * A216856 A040023 A109683

Adjacent sequences: A359734 A359735 A359736 * A359738 A359739 A359740

Keyword

nonn,base

Author

M. F. Hasler and Eric Angelini, Jan 12 2023

Status

approved