A302244 Length of longest run of primes in any of the four diagonals starting from the center of a square number spiral with n at the center.

1, 3, 0, 2, 0, 3, 0, 6, 0, 1, 0, 5, 0, 2, 0, 2, 0, 8, 0, 1, 0, 1, 0, 4, 0, 4, 0, 2, 0, 3, 0, 1, 0, 1, 0, 3, 0, 8, 0, 1, 0, 20, 0, 4, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 13, 0, 1, 0, 2, 0, 3, 0, 7, 0, 1, 0, 4, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2

Offset

0,2

Comments

As in A299207, the center number is not considered in the run.

Note that a(n)=0 for all even n>0.

Links

Robert Price, Table of n, a(n) for n = 0..10000

Wikipedia, Ulam spiral

Index entries for sequences related to spirals

Example

For n=3:
+-------------------------------+
| 39   38  37  36  35   34   33 |
|    +---------------------+    |
| 40 | 19  18  17  16   15 | 32 |
|    |    +-----------+    |    |
| 41 | 20 | 7   6   5 | 14 | 31 |
|    |    |   +---+   |    |    |
| 42 | 21 | 8 | 3   4 | 13 | 30 |
|    |    |   +-------+    |    |
| 43 | 22 | 9  10  11   12 | 29 |
|    |    +----------------+    |
| 44 | 23  24  25  26   27   28 |
|    +--------------------------+
| 45   46  47  48  49   50   51
+--------------------------------
The encountered primes are 7, 19 in the NW direction, 5 in the NE direction and 11 in the SE direction, so a(3) = 2.

Crossrefs

Cf. A215471, A299207.

Sequence in context: A035464 A194669 A364570 * A019746 A112574 A318652

Adjacent sequences: A302241 A302242 A302243 * A302245 A302246 A302247

Keyword

nonn

Author

Robert Price, Apr 03 2018

Status

approved