|
Search: id:A161586
|
|
|
| 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. |
|
+0
2
|
|
| 0, 1320, 157080, 18691211, 2224097040, 264648856560, 31490989833611, 3747163141343160, 445880922830002440, 53056082653628947211, 6313227954859014715680, 751221070545569122218720, 89388994166967866529312011, 10636539084798630547865910600
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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.
|
|
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: A067206 A157266 A069737 this_sequence A013641 A092088 A068302
Adjacent sequences: A161583 A161584 A161585 this_sequence A161587 A161588 A161589
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 14 2009
|
|
EXTENSIONS
|
Edited, extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2009
|
|
|
Search completed in 0.002 seconds
|
