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A083713
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a(n) = (8^n - 1)*3/7.
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8
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0, 3, 27, 219, 1755, 14043, 112347, 898779, 7190235, 57521883, 460175067, 3681400539, 29451204315, 235609634523, 1884877076187, 15079016609499, 120632132875995, 965057063007963, 7720456504063707, 61763652032509659
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OFFSET
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0,2
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COMMENTS
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Fixed points of the mapping defined by A067585. In binary these numbers show a regular pattern: 0, 11, 11011, 11011011, 11011011011, etc.
terms of A173593 beginning and ending with digits '11' in binary representation;
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LINKS
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FORMULA
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Recursion: a(0) = 0, a(n+1) = (((a(n)*2)*2+1)*2+1).
a(0)=0, a(1)=3, a(n) = 9*a(n-1) - 8*a(n-2). - Harvey P. Dale, Jun 06 2013
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EXAMPLE
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Octal..........decimal:
0....................0
3....................3
33..................27
333................219
3333..............1755
33333............14043
333333..........112347
3333333.........898779
33333333.......7190235
333333333.....57521883
3333333333...460175067
etc. (End)
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MATHEMATICA
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(3/7)(8^Range[0, 20]-1) (* or *) LinearRecurrence[{9, -8}, {0, 3}, 30] (* or *) NestList[8#+3&, 0, 30] (* Harvey P. Dale, Jun 06 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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