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A001387 Decimal encoding of a binary "look and say" sequence (A005150). 6
1, 11, 101, 111011, 11110101, 100110111011, 111001011011110101, 111100111010110100110111011, 100110011110111010110111001011011110101, 1110010110010011011110111010110111100111010110100110111011 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

I conjecture that the ratio r(n) of the number of "1"s to the number of "0"s in a(n) converges to 5/3 (or some nearby limit). - Joseph L. Pe, Jan 31 2003

The ratio r(n) of the number of "1"s to the number of "0"s in a(n) actually converges to [(101 - 5\sqrt{93})a^2 + (139 - 13\sqrt{93})a - 76]/108, where a = (116 + 12\sqrt{93})^{1/3}. This ratio has decimal expansion 1.6657272222676... - Nathaniel Johnston, Nov 07 2010

LINKS

John Cerkan, Table of n, a(n) for n = 1..17

Torsten Sillke, The binary form of Conway's sequence

Nathaniel Johnston, The Binary "Look-and-Say" Sequence [From Nathaniel Johnston, Nov 07 2010]

EXAMPLE

To get the 5th term, for example, note that 4th term has three (11 in binary!) 1's, one (1) 0 and two (10) 1's, giving 11 1 1 0 10 1.

MATHEMATICA

a[1] := 1; a[n_] := a[n] = FromDigits[Flatten[{IntegerDigits[Length[#], 2], First[#]}& /@ Split[IntegerDigits[a[n-1]]]]]; Map[a, Range[20]] (* Peter J. C. Moses, Mar 24 2013 *)

CROSSREFS

Cf. A005150, A049194.

Sequence in context: A156668 A103992 A185949 * A247863 A180280 A100580

Adjacent sequences:  A001384 A001385 A001386 * A001388 A001389 A001390

KEYWORD

nonn,base

AUTHOR

Thomas L. York

STATUS

approved

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Last modified June 28 14:30 EDT 2017. Contains 288838 sequences.