Tomas Rigaux has authored 2 sequences.
A362016
Maximal number of unmarked cells with at least 3 marked neighboring cells in the n X n kings' graph.
Original entry on oeis.org
0, 1, 4, 8, 13, 20, 28, 38, 50, 61, 75, 90, 108, 124, 139
Offset: 1
a(2) = 1, as the only pattern is
.X
XX
a(9) = 50, with a similar pattern to prove that r >= 2/3:
X.......X
.XXXXXXX.
X.......X
.........
XXXXXXXXX
.........
X.......X
.XXXXXXX.
X.......X
a(10) = 61, and a pattern that reaches that is
X..X...X..
XX.X.X.X.X
..........
.X.XX.X.XX
XX....X...
....X....X
X.XX..XX.X
X....X....
...X....XX
XX.X.XX.X.
If we only want 1 marked neighbor, we get n^2 -
A075561(n).
A330671
Largest number whose base-n expansion cannot be subdivided to form a sequence of numbers which ordered form a multiple of n+1 when using +, *, and ().
Original entry on oeis.org
1, 7, 13, 41, 206, 335, 503, 2746, 9898, 13938, 20588, 28390, 38007, 50366, 1006418, 82650, 1865809, 1738855, 2879137, 4024861, 5135433, 5585431, 7932985
Offset: 2
For n = 2, the binary notation of a number cannot contain any 0, as you could then construct 0 by multiplying all the digits together, so the only candidates are 1, 11, 111, 1111 (or 1, 3, 7, 15, ... in base 10).
Out of those, if you have at least 2 digits, the number contains the substring '11', which can be multiplied by all the other digits to give 11 (or 3 in base 10), which gives a(2) = 1 as the largest and only solution.
For n = 4, a(n) = 13 can be easily checked using the fact that the base-4 expansion of a valid number cannot contain a 2 and a 3 next to each other, as 2+3 = 5 = n+1.
For n = 10, 12345 is not a valid number as 1+2*3*4*5 = 121 = 11*11.
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