A359736 Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = dist(a(n), SQUARES) has the same sequence of digits.

0, 10, 1, 2, 6, 42, 20, 7, 11, 4, 56, 3, 5, 21, 30, 43, 12, 31, 14, 8, 13, 9, 29, 19, 15, 18, 22, 17, 24, 32, 72, 26, 28, 90, 23, 91, 35, 109, 37, 41, 48, 73, 27, 34, 50, 57, 38, 40, 33, 47, 71, 51, 62, 55, 66, 89, 112, 16, 79, 39, 130, 63, 46, 44, 65, 25, 135

Offset

0,2

Comments

In the definition, dist(a(n), SQUARES) = A053188(a(n)) is the distance of a(n) from the nearest square. "... has the same 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, 2, 3, 11, 9, 12, 4, 7, 19, 21, 1, 8, 16, 20, 18, 24, ...)

Links

Table of n, a(n) for n=0..66.

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

Example

Below, row "s" lists the closest square to a(n) and row "d" the absolute difference |a(n)-s|. 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  10   1   2   6  42  20   7  11   4  56   3   5  21  30 ...
  s :  0   9   1   1   4  36  16   9   9   4  49   4   6  25  25 ...
  d :  0   1   0   1   2   6   4   2   2   0   7   1   1   4   5 ...

Prog

(PARI) spine(x->x^2, 200) \\ See A359734 for spine()

Crossrefs

Cf. A053188 (distance from the nearest square), A000290 (the squares).

Cf. A359734, A359737 (similar for primes and Fibonacci numbers).

Sequence in context: A085764 A090555 A283393 * A010179 A174209 A366165

Adjacent sequences: A359733 A359734 A359735 * A359737 A359738 A359739

Keyword

nonn,base

Author

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

Status

approved