Re: Find count of binary number pattern within concatenated number

• To: mathgroup at smc.vnet.net
• Subject: [mg91153] Re: Find count of binary number pattern within concatenated number
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 7 Aug 2008 04:42:42 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g7bqom\$moc\$1@smc.vnet.net>

```Diana wrote:

> Can someone tell me how to find the count of the occurrences of "1101"
> within "11011100101110111100010011010101111001101" generated with the
> FromDigits statements below? I will be increasing "n".
>
> n=13
>
> FromDigits[Flatten[IntegerDigits[Range[n],2]]]
>
> 11011100101110111100010011010101111001101.
>
> FromDigits[IntegerDigits[n, 2]]
>
> 1101

Here is two almost identical versions of the counting function: the
first one seeks for overlapping sequences, the second looks only for
non-overlapping sequences. Of course the results might be very different
for a same number.

(* Overlapping sequences *)
myCount[n_Integer] :=
Module[{nb2 = IntegerDigits[n, 2]},
Flatten[Position[
Partition[Flatten[IntegerDigits[Range[n], 2]], Length[nb2], 1],
nb2]]]

myCount[13]

{1, 12, 25, 38}

(* Non-Overlapping sequences *)
myCount[n_Integer] :=
Module[{nb2 = IntegerDigits[n, 2]},
Flatten[Position[
Partition[Flatten[IntegerDigits[Range[n], 2]], Length[nb2]],
nb2]]]

myCount[13]

{1, 7}

Regards,
-- Jean-Marc

```

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