login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A230962 Values of x such that x^2 + y^2 = 73^n with x and y coprime and 0 < x < y. 2
3, 48, 296, 721, 10072, 213785, 1958709, 7613760, 21165597, 894454032, 12278087704, 59926173839, 62518379032, 3374316625735, 58552907681096, 416603004343680, 1261259807092797, 10231862403603888, 255781764375436389, 2697529798981443601, 11543491568219853608 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The corresponding y-values are in A230963.
LINKS
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) = min(abs(Re((3+8i)^n)), abs(Im((3+8i)^n))).
a(n) = abs(Re(3+8i)^n) if and only if 1/4 < frac(n*arctan(8/3)/Pi) < 3/4.
(End)
EXAMPLE
a(3) = 296 because 296^2 + 549^2 = 389017 = 73^3.
MAPLE
f:=n -> min([abs@Re, abs@Im]((3+8*I)^n)):
map(f, [$1..50]); # Robert Israel, Mar 31 2017
MATHEMATICA
Table[Select[PowersRepresentations[73^n, 2, 2], CoprimeQ@@#&][[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Mar 02 2014 *)
Table[Min[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([min(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
Sequence in context: A162333 A003878 A219056 * A073982 A356644 A354132
KEYWORD
nonn
AUTHOR
Colin Barker, Nov 02 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)