[seqfan] A Pi-day self-chunking sequence

Eric Angelini Eric.Angelini at kntv.be
Mon Mar 14 16:21:23 CET 2011

Hello Seqfans,
[crossposted to oulipo at quatramaran dot ens dot fr]


P = 2,3,4,5,1,6,7,8,14,9,20,22,23,21,15,10,11,12,13,16,19,17,18,30,31,33,34,32,24,25,27,28,29,35,37,26,36,38,39,40,41,42,43,44,46,47,48,49,60,45,50,51,52,54,55,56,57,58,53,59,...

Read P from left to right:

P = 2,3,4,5,1,6,7,8,14,9,20,22,23,21,15,10,11,12,13,16,19,17,

Stop immediately when you bump into the first digit of Pi:

P = 2,3

Put a vertical stroke behind the said digit:

P = 2,3|

Proceed reading from there, and stop again when you bump
into the next digit of Pi - drawing another vertical stroke

P = 2,3|,4,5,1|

Go on like this - drawing a stroke every time you bump into
"the next digit of Pi":

P = 2,3|,4,5,1|,6,7,8,14|,9,20,22,23,21|,15|,10,11,12,13,16,19|,17...

The size of each chunk is given by P itself:

P = 2,3|,4,5,1|,6,7,8,14|,9,20,22,23,21|,15|,10,11,12,13,16,19|,17...
     2     3       4            5        1           6

(the size of a chunk is the amount of integers it contains)

P is (by construction), a permutation of N (as we "always use
the smallest integer not yet present in P and not leading to
a contradiction")

P was computed by hand after a lot of tries - I hope I didn't
leave too many errors...

Best Pi-day,

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