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Search: id:A161591
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| A161591 |
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The list of the B values in the common solutions to the 2 equations 13*k+1=A^2, 17*k+1=B^2. |
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4
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| 1, 16, 239, 3569, 53296, 795871, 11884769, 177475664, 2650250191, 39576277201, 590993907824, 8825332340159, 131788991194561, 1968009535578256, 29388354042479279, 438857301101610929, 6553471162481684656, 97863210136123658911, 1461394680879373199009
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The 2 equations are equivalent to the Pell equation x^2-221*y^2=1,
with x=(221*k+15)/2 and y= A*B/2, case C=13 in A160682.
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FORMULA
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B(t+2)=15*B(t+1)-B(t).
B(t)=((221+17*w)*((15+w)/2)^(t-1)+(221-17*w)*((15-w)/2)^(t-1))/442 where w=sqrt(221).
B(t) = floor of ((221+17*w)*((15+w)/2)^(t-1))/442 = A078364(t-2)+A078364(t-1).
G.f.: x*(1+x)/(1-15*x+x^2).
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MAPLE
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t:=0: for b from 1 to 1000000 do a:=sqrt((13*b^2+4)/17):
if (trunc(a)=a) then t:=t+1: n:=(b^2-1)/17: print(t, a, b, n): end if: end do:
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PROGRAM
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(Other) sage: [(lucas_number2(n, 15, 1)-lucas_number2(n-1, 15, 1))/13 for n in xrange(1, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
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CROSSREFS
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Cf. A160682 (sequence of A), A161584 (sequence of k).
Sequence in context: A028340 A119463 A111096 this_sequence A103975 A060198 A097829
Adjacent sequences: A161588 A161589 A161590 this_sequence A161592 A161593 A161594
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KEYWORD
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nonn,new
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AUTHOR
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Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 14 2009
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EXTENSIONS
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Edited, extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2009
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