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A112627
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Decimal equivalent of number defined by last k bits of the infinite binary string ...0011001100110011 (numbers with leading zeros omitted).
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11
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1, 3, 19, 51, 307, 819, 4915, 13107, 78643, 209715, 1258291, 3355443, 20132659, 53687091, 322122547, 858993459, 5153960755, 13743895347, 82463372083, 219902325555, 1319413953331, 3518437208883, 21110623253299
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| G.f.: (1+2*x)/(1-x-16*x^2+16*x^3) [according to Superseeker].
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EXAMPLE
| 1 = 1
11 = 3
10011 = 19
110011 = 51
100110011 = 307
1100110011 = 819
...
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MATHEMATICA
| t = {}; lst = First@RealDigits[ N[1/5, 100], 2]; Do[ If[ lst[[n]] == 1, AppendTo[t, FromDigits[ Reverse@Take[lst, n], 2]]], {n, 49}]; t
(* The first line establishes the binary expansion of 1/5 to 100 places (A021913, except for start). The loop extracts the first n terms in this sequence and if it ends in "1", reverses digits and converts to decimal. *)
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CROSSREFS
| Sequence in context: A099007 A023280 A054697 * A100697 A134268 A088798
Adjacent sequences: A112624 A112625 A112626 * A112628 A112629 A112630
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), based on email from Artur Jasinski (grafix(AT)csl.pl), with assistance from Dean Hickerson, Ray Chandler and Robert G. Wilson v, Dec 27 2005
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