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

8, 55, 549, 5280, 44403, 325008, 2685304, 27358559, 241709752, 1870181225, 12766175931, 138963670560, 1291487885997, 10519458225072, 74032715923371, 690521409218881, 6773980286782088, 57975621715535095, 433109386513469096, 3345582274543898400

Offset

1,1

Comments

The corresponding x-values are in A230962.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Chris Busenhart, Lorenz Halbeisen, Norbert Hungerbühler, and Oliver Riesen, On primitive solutions of the Diophantine equation x^2+ y^2= M, Eidgenössische Technische Hochschule (ETH Zürich, Switzerland, 2020).

Formula

From Robert Israel, Mar 31 2017: (Start)

a(n) = max(abs(Re((3+8i)^n)), abs(Im((3+8i)^n))).

a(n) = abs(Im(3+8i)^n) if and only if 1/4 < frac(n*arctan(8/3)/Pi) < 3/4.(End)

Example

a(3)=549 because 296^2 + 549^2 = 389017 = 73^3.

Maple

f:=n ->  max([abs@Re, abs@Im]((3+8*I)^n)):
map(f, [$1..50]); # Robert Israel, Mar 31 2017

Mathematica

Table[Max[Abs[Re[(3 + 8I)^n]], Abs[Im[(3 + 8I)^n]]], {n, 30}] (* Indranil Ghosh, Mar 31 2017, after formula by Robert Israel *)

Prog

(Python)
from sympy import I, re, im
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

Crossrefs

Cf. A230962.

Cf. A188949, A230623, A230645, A230711, A230713, A230744, A230760, A230842.

Sequence in context: A019484 A108984 A264342 * A209114 A264644 A144748

Adjacent sequences: A230960 A230961 A230962 * A230964 A230965 A230966

Keyword

nonn

Author

Colin Barker, Nov 02 2013

Status

approved