login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160580 Positive numbers y such that y^2 is of the form x^2+(x+457)^2 with integer x. 3
325, 457, 877, 1073, 2285, 4937, 6113, 13253, 28745, 35605, 77233, 167533, 207517, 450145, 976453, 1209497, 2623637, 5691185, 7049465, 15291677, 33170657, 41087293, 89126425, 193332757, 239474293, 519466873, 1126825885, 1395758465 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(-204, a(1)) and (A129642(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+457)^2 = y^2.

lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).

lim_{n -> infinity} a(n)/a(n-1) = (601+276*sqrt(2))/457 for n mod 3 = {0, 2}.

lim_{n -> infinity} a(n)/a(n-1) = (213651+31850*sqrt(2))/457^2 for n mod 3 = 1.

LINKS

Table of n, a(n) for n=1..28.

FORMULA

a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=325, a(2)=457, a(3)=877, a(4)=1073, a(5)=2285, a(6)=4937.

G.f.: (1-x)*(325+782*x+1659*x^2+782*x^3+325*x^4) / (1-6*x^3+x^6).

a(3*k-1) = 457*A001653(k) for k >= 1.

EXAMPLE

(-204, a(1)) = (-204, 325) is a solution: (-204)^2+(-204+457)^2 = 41616+64009 = 105625 = 325^2.

(A129642(1), a(2)) = (0, 457) is a solution: 0^2+(0+457)^2 = 208849 = 457^2.

(A129642(3), a(4)) = (495, 1073) is a solution: 495^2+(495+457)^2 = 245025+906304 = 1151329 = 1073^2.

PROG

(PARI) {forstep(n=-204, 10000000, [3, 1], if(issquare(2*n^2+914*n+208849, &k), print1(k, ", ")))}

CROSSREFS

Cf. A129642, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A160581 (decimal expansion of (601+276*sqrt(2))/457), A160582 (decimal expansion of (213651+31850*sqrt(2))/457^2).

Sequence in context: A025313 A025286 A025304 * A158272 A183645 A299708

Adjacent sequences:  A160577 A160578 A160579 * A160581 A160582 A160583

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Jun 08 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 17:45 EST 2019. Contains 329287 sequences. (Running on oeis4.)