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A230963 Values of y such that x^2 + y^2 = 73^n with x and y coprime and 0 < x < y.

%I A230963 #26 May 08 2021 08:36:39
%S A230963 8,55,549,5280,44403,325008,2685304,27358559,241709752,1870181225,
%T A230963 12766175931,138963670560,1291487885997,10519458225072,74032715923371,
%U A230963 690521409218881,6773980286782088,57975621715535095,433109386513469096,3345582274543898400
%N A230963 Values of y such that x^2 + y^2 = 73^n with x and y coprime and 0 < x < y.
%C A230963 The corresponding x-values are in A230962.
%H A230963 Robert Israel, <a href="/A230963/b230963.txt">Table of n, a(n) for n = 1..1000</a>
%H A230963 Chris Busenhart, Lorenz Halbeisen, Norbert Hungerbühler, and Oliver Riesen, <a href="https://people.math.ethz.ch/~halorenz/publications/pdf/Miniatur.pdf">On primitive solutions of the Diophantine equation x^2+ y^2= M</a>, Eidgenössische Technische Hochschule (ETH Zürich, Switzerland, 2020).
%F A230963 From _Robert Israel_, Mar 31 2017: (Start)
%F A230963 a(n) = max(abs(Re((3+8i)^n)), abs(Im((3+8i)^n))).
%F A230963 a(n) = abs(Im(3+8i)^n) if and only if 1/4 < frac(n*arctan(8/3)/Pi) < 3/4.(End)
%e A230963 a(3)=549 because 296^2 + 549^2 = 389017 = 73^3.
%p A230963 f:=n ->  max([abs@Re,abs@Im]((3+8*I)^n)):
%p A230963 map(f, [$1..50]); # _Robert Israel_, Mar 31 2017
%t A230963 Table[Max[Abs[Re[(3 + 8I)^n]], Abs[Im[(3 + 8I)^n]]], {n, 30}] (* _Indranil Ghosh_, Mar 31 2017, after formula by _Robert Israel_ *)
%o A230963 (Python)
%o A230963 from sympy import I, re, im
%o A230963 print([max(abs(re((3 + 8*I)**n)), abs(im((3 + 8*I)**n))) for n in range(1, 31)]) # _Indranil Ghosh_, Mar 31 2017, after formula by _Robert Israel_
%Y A230963 Cf. A230962.
%Y A230963 Cf. A188949, A230623, A230645, A230711, A230713, A230744, A230760, A230842.
%K A230963 nonn
%O A230963 1,1
%A A230963 _Colin Barker_, Nov 02 2013