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A161583 The list of the k values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2. 3
0, 17, 4896, 1405152, 403273745, 115738159680, 33216448554432, 9533004996962321, 2735939217679631712, 785205022469057339040, 225351105509401776672785, 64674982076175840847750272, 18561494504756956921527655296, 5327084247883170460637589319697 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The 2 equations are equivalent to the Pell equation x^2-285*y^2=1,

with x=(285*k+17)/2 and y=A*B/2, case C=15 in A160682.

LINKS

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

FORMULA

k(t+3)=288*(k(t+2)-k(t+1))+k(t).

k(t)=((17+w)*((287+17*w)/2)^(t-1)+(17-w)*((287-17*w)/2)^(t-1))/570 where w=sqrt(285).

k(t) = floor of ((17+w)*((287+17*w)/2)^(t-1))/570;

G.f.: -17*x^2/((x-1)*(x^2-287*x+1)).

MAPLE

t:=0: for n from 0 to 1000000 do a:=sqrt(15*n+1): b:=sqrt(19*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, A161595 (sequence of A), A161599 (sequence of B)

Sequence in context: A194015 A015058 A015034 * A013722 A238610 A052286

Adjacent sequences:  A161580 A161581 A161582 * A161584 A161585 A161586

KEYWORD

nonn

AUTHOR

Paul Weisenhorn, Jun 14 2009

EXTENSIONS

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

STATUS

approved

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Last modified October 18 12:24 EDT 2018. Contains 316321 sequences. (Running on oeis4.)