|
|
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
|
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1+2*x)/(1-x-16*x^2+16*x^3).
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
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|