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Decimal representation of the n-th iteration of Conway’s Game of Life starting with two adjacent two-way infinite rows of ON cells.
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%I #20 Apr 05 2016 09:15:45

%S 3,9,63,129,903,2193,15351,32769,229383,5577073,3899511,8421633,

%T 58951431,143167761,1002174327,2147483649,15032385543,36507222033,

%U 25550554231,551903297793,3863323084551,9382356062481,65676492437367,140739635904513,985177451331591,2392573810376721,16748016672637047,36170086427459841,25319060499221887,614891469266817297,4304240284867721079,9223372036854775809

%N Decimal representation of the n-th iteration of Conway’s Game of Life starting with two adjacent two-way infinite rows of ON cells.

%C Empirical observations:

%C The sequence starting with a single row of ON cells is A266382.

%C Every 2^n-1 step of iteration generates the biggest gap (g) between two rows.

%C The prime factors for numbers in this sequence up to the 31st term are: 3,7,11,17,19,31,43,257,331,5419,65537,715827883,77158673929.

%e 0th iteration = 11 = 3, 1st iteration = 1001 = 9, 2nd iteration = 111111 = 63, 3rd iteration = 10000001 = 129, 4th iteration = 1110000111 = 903, 5th iteration = 100010010001, 6th iteration = 11101111110111......

%Y Cf. A266382.

%K nonn

%O 0,1

%A _Brook Estifanos_, Mar 08 2016