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

Author

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

Keywords

• nonn
• base

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, ...)

Examples

			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 ...
		

Links

• 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]

Crossrefs

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

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

Programs

PARI

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