A269961 Decimal representation of the n-th iteration of Conway’s Game of Life starting with two adjacent two-way infinite rows of ON cells.

3, 9, 63, 129, 903, 2193, 15351, 32769, 229383, 5577073, 3899511, 8421633, 58951431, 143167761, 1002174327, 2147483649, 15032385543, 36507222033, 25550554231, 551903297793, 3863323084551, 9382356062481, 65676492437367, 140739635904513, 985177451331591, 2392573810376721, 16748016672637047, 36170086427459841, 25319060499221887, 614891469266817297, 4304240284867721079, 9223372036854775809

Offset

0,1

Comments

Empirical observations:

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

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

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.

Links

Table of n, a(n) for n=0..31.

Example

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......

Crossrefs

Cf. A266382.

Sequence in context: A243425 A018513 A143761 * A064703 A085435 A121696

Adjacent sequences: A269958 A269959 A269960 * A269962 A269963 A269964

Keyword

nonn

Author

Brook Estifanos, Mar 08 2016

Status

approved