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