login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161586 The list of the k values in the common solutions to the 2 equations 9*k+1=A^2, 13*k+1=B^2. 1
0, 1320, 157080, 18691211, 2224097040, 264648856560, 31490989833611, 3747163141343160, 445880922830002440, 53056082653628947211, 6313227954859014715680, 751221070545569122218720, 89388994166967866529312011, 10636539084798630547865910600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The 2 equations are equivalent to the Pell equation x^2-117*y^2=1,

with x=(117*k+11)/2 and y=A*B/2, case C=9 in A160682.

LINKS

Table of n, a(n) for n=1..14.

Index entries for linear recurrences with constant coefficients, signature (120,-120,1).

FORMULA

k(t+3)=120*(k(t+2)-k(t+1))+k(t).

k(t)=((11+w)*((119+11*w)/2)^(t-1)+(11-w)*((119-11*w)/2)^(t-1))/234 where w=sqrt(117).

k(t) = floor of ((11+w)*((119+11*w)/2)^(t-1))/234;

G.f.: -11*x^2/((x-1)*(x^2-119*x+1)).

MAPLE

t:=0: for n from 0 to 1000000 do a:=sqrt(9*n+1): b:=sqrt(13*n+1):

if (trunc(a)=a) and (trunc(b)=b) then t:=t+1: print(t, n, a, b): end if: end do:

CROSSREFS

Cf. A160682, A078922 (sequence of A), A097783 (sequence of B).

Sequence in context: A069737 A185464 A323802 * A013641 A295449 A092088

Adjacent sequences:  A161583 A161584 A161585 * A161587 A161588 A161589

KEYWORD

nonn,easy

AUTHOR

Paul Weisenhorn, Jun 14 2009

EXTENSIONS

Edited, extended by R. J. Mathar, Sep 02 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 30 05:12 EST 2021. Contains 349419 sequences. (Running on oeis4.)