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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Brook Estifanos

Brook Estifanos's wiki page.

Brook Estifanos has authored 2 sequences.

A270072 Decimal representation of the n-th iteration of the Conway’s game of life starting with four adjacent rows of lines turned on to positive and negative infinity.

Original entry on oeis.org

15, 33, 231, 561, 3735, 8673, 58407, 146673, 951831, 2200161, 15007527, 37618161, 243401751, 562961505, 3835839783, 9654230001, 62277025815, 1438881404513, 981400027431, 2471753680881, 15945066090519, 38848671944801, 251274914238759, 633024492828657, 4081389310836759, 589338770407521, 6431706870343299, 161989104772314217, 1044976403211096087
Offset: 0

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Author

Brook Estifanos, Mar 09 2016

Keywords

Comments

It is conjectured that every term has a prime factor that does not divide any previous term.

Examples

			0th iteration = 1111 = 15, 1st iteration = 100001 = 33, 2nd iteration = 11100111 = 231, 3rd iteration = 1000110001 = 561, 4th iteration = 111010010111 = 3735, 5th iteration = 10000111100001 = 8673, ... .

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.

Original entry on oeis.org

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

Views

Author

Brook Estifanos, Mar 08 2016

Keywords

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.

Examples

			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.

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