3
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The sequence is:

4,7,7,0,1,1,4,8,3,2,3,9,4,1,5,3,0,6,4,5,0,5,1,0,9,1,2,7,7,1,4,9,5,5,6,9,5,1,?

It's very simple indeed you won't need to do any calculation, but you may need to do a little one, good luck. Yes you may really need to read this hint.

Hint1:

Three things make up it, one of them is the first of Good Boy. A cat tamed the boy. The third one is an acronym relating to computer networks.

Hint2:

It is neither due to Euler, nor by Apery.

Hint3:[New]

Some constant perhaps?

Edit: Hint edited.

Edit2: Ok I may add other hints if you comment something (maybe the problem you're facing or which type of hint should be there).

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  • $\begingroup$ Hint 2 tells me it's something to do with the Riemann zeta function $\endgroup$ – Rand al'Thor May 16 '15 at 9:23
  • $\begingroup$ Is Hint 1 anything to do with this? $\endgroup$ – Rand al'Thor May 16 '15 at 11:46
  • $\begingroup$ @randal'thor nope, don't go on the meanings really of it $\endgroup$ – RE60K May 16 '15 at 16:45
  • $\begingroup$ Based on the hints: Is it really a "number-sequence" puzzle or rather a riddle/cryptogram? i.e. what is the next letter in "This is a wonderful puzzl" is not a letter-sequence puzzle! $\endgroup$ – BmyGuest May 18 '15 at 15:47
  • $\begingroup$ @BmyGuest Well I'm not well going into English. I can only say that they are interrelated to each other and there's no riddle cryptogram. They form together something I may call it a series, if you agree. $\endgroup$ – RE60K May 18 '15 at 15:48
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In my opinion this is a mean puzzle that I just happened to solve because I got lucky. It is unsolvable without the hints.

The answer is:

9

Reasoning:

The number sequence is Catalan's constant backwards, starting arbitrarily 39 digits from the decimal point.

Hint 1:

It is referred to by a capital G in mathematics, a cat tamed the boy (refers to cata, not sure why), and LAN stands for local area network.

Hint 2 and 3:

It is a constant that isn't Euler's or Apery's.

How I figured it out:

The hints and random googling made me sure the answer had something to do with Catalan many days ago, but no matter what transformations I did I couldn't find the connection. After revisiting, by chance I happened to notice the constant on the Wikipedia page had the same number of digits (39) as the puzzle and from there I saw the connection. A bit mean but I guess solvable.

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