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5, 33, 257, 2049, 16385, 131073, 1048577, 8388609, 67108865, 536870913, 4294967297, 34359738369, 274877906945, 2199023255553, 17592186044417, 140737488355329, 1125899906842625, 9007199254740993, 72057594037927937
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OFFSET
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0,1
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COMMENTS
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An Engel expansion of 2 to the base 8 as defined in A181565, with the associated series expansion 2 = 8/5 + 8^2/(5*33) + 8^3/(5*33*257) + 8^4/(5*33*257*2049) + .... Cf. A087289 and A199493. - Peter Bala, Oct 29 2013
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LINKS
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FORMULA
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a(n) = 8*a(n-1)-7.
a(n) = 9*a(n-1)-8*a(n-2).
G.f.: (5-12*x)/((1-x)*(1-8*x)).
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MATHEMATICA
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4*8^Range[0, 20]+1 (* or *) LinearRecurrence[{9, -8}, {5, 33}, 20] (* Harvey P. Dale, Mar 18 2018 *)
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PROG
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(Magma) [4*8^n+1: n in [0..30]];
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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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