

A161588


The list of the k values in the common solutions to the 2 equations 11*k+1=A^2, 15*k+1=B^2.


1



0, 13, 2184, 364728, 60907405, 10171171920, 1698524803248, 283643470970509, 47366761127271768, 7909965464783414760, 1320916865857702993165, 220585206632771616443808, 36836408590807002243122784, 6151459649458136602985061133, 1027256925050918005696262086440
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OFFSET

1,2


COMMENTS

The 2 equations are equivalent to the Pell equation x^2165*y^2=1,
with x=(165*k+13)/2 and y=A*B/2, case C=11 in A160682.


LINKS

Table of n, a(n) for n=1..15.
Index entries for linear recurrences with constant coefficients, signature (168,168,1).


FORMULA

k(t+3)=168*(k(t+2)k(t+1))+k(t).
k(t)=((13+w)*((167+13*w)/2)^(t1)+(13w)*((16713*w)/2)^(t1))/330 where w=sqrt(165).
k(t) = floor of ((13+w)*((167+13*w)/2)^(t1))/330;
G.f.: 13*x^2/((x1)*(x^2167*x+1)).


MAPLE

t:=0: for n from 0 to 1000000 do a:=sqrt(11*n+1): b:=sqrt(15*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, A085260 (sequence of A), A126816 (sequence of B).
Sequence in context: A221823 A075601 A325216 * A221927 A013718 A145187
Adjacent sequences: A161585 A161586 A161587 * A161589 A161590 A161591


KEYWORD

nonn,easy


AUTHOR

Paul Weisenhorn, Jun 14 2009


EXTENSIONS

Edited, extended by R. J. Mathar, Sep 02 2009


STATUS

approved



