A347337 The prime numbers ordered by their distance from the origin of a square spiral which starts at 1. If two or more primes have the same distance from the origin the smaller prime appears first.

2, 3, 5, 7, 11, 19, 23, 13, 17, 29, 41, 47, 53, 61, 31, 37, 43, 59, 67, 71, 79, 97, 107, 73, 83, 89, 103, 109, 113, 127, 139, 151, 163, 137, 149, 101, 191, 131, 167, 173, 179, 193, 233, 281, 251, 263, 283, 157, 181, 199, 223, 229, 269, 277, 317, 353, 313, 331, 337, 349, 197, 211, 227, 239

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Example

The square spiral is numbered as follows:
.
  17--16--15--14--13   .
   |               |   .
  18   5---4---3  12   29
   |   |       |   |   |
  19   6   1---2  11   28
   |   |           |   |
  20   7---8---9--10   27
   |                   |
  21--22--23--24--25--26
.
a(1) = 2 as this is the only prime a distance of 1 unit from the origin.
a(2) = 3, a(3) = 5, a(4) = 7. All of these primes are a distance of
sqrt(2) units from the origin, so they are listed with the smaller primes first.
a(6) = 19 as this is 2 units from the origin, the same as a(5) = 11. This is the first prime that appears out of natural order as both 13 and 17 are sqrt(8) units, which is greater than 2 units, from the origin.

Crossrefs

Cf. A000040, A063826, A214664, A214665, A136626, A115258, A331027.

Sequence in context: A069749 A081889 A078139 * A210186 A120628 A322471

Adjacent sequences: A347334 A347335 A347336 * A347338 A347339 A347340

Keyword

nonn

Author

Scott R. Shannon, Aug 27 2021

Status

approved