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Search: id:A159678
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| A159678 |
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The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 7*n(j)+1=a(j)*a(j) and 9*n(j)+1=b(j)*b(j) with positiv integer numbers. |
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+0
3
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| 1, 17, 271, 4319, 68833, 1097009, 17483311, 278635967, 4440692161, 70772438609, 1127918325583, 17975920770719, 286486814005921, 4565813103324017, 72766522839178351, 1159698552323529599, 18482410314337295233, 294558866477073194129, 4694459453318833810831
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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The a(j) recurrence is a(1)=1; a(2)=15; a(t+2)=16*a(t+1)-a(t)
resulting in terms 1, 15, 239, 3809
The b(j) recurrence is b(1)=1; b(2)=17; b(t+2)=16*b(t+1)-b(t)
resulting in terms 1, 17, 271, 4319 as listed above
The n(j) recurrence is n(0)=n(1)=0; n(2)=32; n(t+3)=255*(n(t+2)-n(t+1))+n(t)
resulting in terms 0, 0, 32, 8160, 2072640
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MAPLE
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for a from 1 by 2 to 100000 do b:=sqrt((9*a*a-2)/7): if (trunc(b)=b) then
n:=(a*a-1)/7: La:=[op(La), a]:Lb:=[op(Lb), b]:Ln:=[op(Ln), n]: end if: end do:
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PROGRAM
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(Other) sage: [(lucas_number2(n, 16, 1)-lucas_number2(n-1, 16, 1))/14 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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A157456
Sequence in context: A135214 A090380 A142898 this_sequence A097830 A131865 A031417
Adjacent sequences: A159675 A159676 A159677 this_sequence A159679 A159680 A159681
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KEYWORD
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nonn
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AUTHOR
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Paul Weisenhorn (paulweisenhorn(AT)online.de), Apr 19 2009
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EXTENSIONS
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More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009
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