cp's OEIS Frontend

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.

%I A347337 #7 Sep 18 2021 16:46:53
%S A347337 2,3,5,7,11,19,23,13,17,29,41,47,53,61,31,37,43,59,67,71,79,97,107,73,
%T A347337 83,89,103,109,113,127,139,151,163,137,149,101,191,131,167,173,179,
%U A347337 193,233,281,251,263,283,157,181,199,223,229,269,277,317,353,313,331,337,349,197,211,227,239
%N 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.
%e A347337 The square spiral is numbered as follows:
%e A347337 .
%e A347337   17--16--15--14--13   .
%e A347337    |               |   .
%e A347337   18   5---4---3  12   29
%e A347337    |   |       |   |   |
%e A347337   19   6   1---2  11   28
%e A347337    |   |           |   |
%e A347337   20   7---8---9--10   27
%e A347337    |                   |
%e A347337   21--22--23--24--25--26
%e A347337 .
%e A347337 a(1) = 2 as this is the only prime a distance of 1 unit from the origin.
%e A347337 a(2) = 3, a(3) = 5, a(4) = 7. All of these primes are a distance of
%e A347337 sqrt(2) units from the origin, so they are listed with the smaller primes first.
%e A347337 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.
%Y A347337 Cf. A000040, A063826, A214664, A214665, A136626, A115258, A331027.
%K A347337 nonn
%O A347337 1,1
%A A347337 _Scott R. Shannon_, Aug 27 2021