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A161586
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The list of the k values in the common solutions to the 2 equations 9*k+1=A^2, 13*k+1=B^2.
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0, 1320, 157080, 18691211, 2224097040, 264648856560, 31490989833611, 3747163141343160, 445880922830002440, 53056082653628947211, 6313227954859014715680, 751221070545569122218720, 89388994166967866529312011, 10636539084798630547865910600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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.
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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)).
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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:
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CROSSREFS
| Cf. A160682, A078922 (sequence of A), A097783 (sequence of B).
Sequence in context: A157266 A069737 A185464 * A013641 A092088 A068302
Adjacent sequences: A161583 A161584 A161585 * A161587 A161588 A161589
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KEYWORD
| nonn
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AUTHOR
| Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 14 2009
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EXTENSIONS
| Edited, extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2009
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