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The 'Look and Say' sequence of the concatenation of the prime numbers A033308.
0

%I #21 Aug 17 2020 22:44:54

%S 1,2,1,3,1,5,1,7,3,1,1,3,1,1,1,7,1,1,1,9,1,2,1,3,1,2,1,9,1,3,1,1,1,3,

%T 1,7,1,4,1,1,1,4,1,3,1,4,1,7,1,5,1,3,1,5,1,9,1,6,1,1,1,6,2,7,1,1,1,7,

%U 1,3,1,7,1,9,1,8,1,3,1,8,2,9,1,7,1,1,1,0,2,1,1,0,1,3,1,1,1,0,1,7

%N The 'Look and Say' sequence of the concatenation of the prime numbers A033308.

%C Concatenate all the decimal prime numbers, see A033308, then describe the resulting infinite string using the 'Look and Say' method of A005150.

%H J. H. Conway and Brady Haran, <a href="https://www.youtube.com/watch?v=ea7lJkEhytA">Look-and-Say Numbers</a> (2014), Numberphile video.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Look-and-say_sequence">Look-and-say sequence</a>.

%e The concatenation of the primes starts "23571113171923293137...".

%e a(1) = 1, a(2) = 2 as there is one '2' at the start of the string.

%e a(9) = 3, a(10) = 1 as the primes '11' and '13' from the substring '1113'. which starts with three 1's.

%Y Cf. A033308, A005150, A001155, A056815, A000040.

%K nonn,base

%O 1,2

%A _Scott R. Shannon_, Aug 15 2020