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A112627 Decimal equivalent of number defined by last k bits of the infinite binary string ...0011001100110011 (numbers with leading zeros omitted). 17
1, 3, 19, 51, 307, 819, 4915, 13107, 78643, 209715, 1258291, 3355443, 20132659, 53687091, 322122547, 858993459, 5153960755, 13743895347, 82463372083, 219902325555, 1319413953331, 3518437208883, 21110623253299, 56294995342131, 337769972052787, 900719925474099 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A182512 is a bisection. - Olena Kachko, Dec 16 2023
LINKS
FORMULA
G.f.: x*(1+2*x)/(1-x-16*x^2+16*x^3).
a(n) = 4^(n-1) - (4 + (-4)^n)/20. - Robert Israel, Sep 02 2014
a(n) = a(n-1)+16*a(n-2)-16*a(n-3) for n>3. - Colin Barker, May 19 2016
EXAMPLE
1 = 1
11 = 3
10011 = 19
110011 = 51
100110011 = 307
1100110011 = 819
...
MAPLE
seq(4^(n-1) - (4 + (-4)^n)/20, n=1..100); # Robert Israel, Sep 02 2014
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. *)
Table[FromDigits[PadLeft[{}, n, {0, 0, 1, 1}], 2], {n, 60}]//Union (* Harvey P. Dale, Mar 15 2016 *)
PROG
(PARI) Vec(x*(1+2*x)/((1-x)*(1-4*x)*(1+4*x)) + O(x^50)) \\ Colin Barker, May 19 2016
CROSSREFS
Cf. A182512.
Sequence in context: A214883 A363697 A239449 * A222185 A265774 A100697
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, based on email from Artur Jasinski, with assistance from Dean Hickerson, Ray Chandler and Robert G. Wilson v, Dec 27 2005
STATUS
approved

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Last modified March 28 13:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)