A299207 Length of longest run of primes in any of the four diagonals starting from the center of a square number spiral with prime(n) at the center.

0, 2, 3, 6, 5, 2, 8, 1, 4, 3, 1, 8, 20, 4, 3, 2, 13, 1, 7, 4, 1, 1, 2, 3, 2, 7, 1, 4, 1, 0, 1, 3, 6, 0, 7, 1, 1, 19, 1, 2, 2, 0, 4, 1, 1, 0, 0, 2, 8, 1, 12, 3, 0, 3, 2, 2, 5, 1, 3, 4, 0, 0, 1, 7, 1, 0, 1, 0, 8, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 7, 1, 1

Offset

1,2

Links

Robert Price, Table of n, a(n) for n = 1..10000

Wikipedia, Ulam spiral

Index entries for sequences related to spirals

Example

For n=1:
  +------------------------+
  | 18   17   16   15   14 |
  |    +--------------+    |
  | 19 |  6    5    4 | 13 |
  |    |    +----+    |    |
  | 20 |  7 |  2    3 | 12 |
  |    |    +---------+    |
  | 21 |  8    9   10   11 |
  |    +-------------------+
  | 22   23   24   25   26
  +-------------------------
None of the four numbers located on the diagonals in NE, NW, SW or SE direction are prime, so a(1) = 0.
.
For n=2:
  +----------------------------------+
  | 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 5 in NE direction, 7, 19, in NW direction and 11 in SE direction, so a(2) = 2.
.
For n=3:
  +--------------------------------------------+
  | 69   68   67   66   65   64   63   62   61 |
  |    +----------------------------------+    |
  | 70 | 41   40   39   38   37   36   35 | 60 |
  |    |    +------------------------+    |    |
  | 71 | 42 | 21   20   19   18   17 | 34 | 59 |
  |    |    |    +--------------+    |    |    |
  | 72 | 43 | 22 |  9    8    7 | 16 | 33 | 58 |
  |    |    |    |    +----+    |    |    |    |
  | 73 | 44 | 23 | 10 |  5    6 | 15 | 32 | 57 |
  |    |    |    |    +---------+    |    |    |
  | 74 | 45 | 24 | 11   12   13   14 | 31 | 56 |
  |    |    |    +-------------------+    |    |
  | 75 | 46 | 25   26   27   28   29   30 | 55 |
  |    |    +-----------------------------+    |
  | 76 | 47   48   49   50   51   52   53   54 |
  |    +---------------------------------------+
  | 77   78   79   80   81   82   83   84   85
  +---------------------------------------------
The encountered primes are 7, 17 in NE direction, 11 in SW direction and 13, 29, 53 in SE direction, so a(3) = 3.

Crossrefs

Cf. A215471.

Sequence in context: A011159 A359623 A091556 * A277330 A072298 A130686

Adjacent sequences: A299204 A299205 A299206 * A299208 A299209 A299210

Keyword

nonn

Author

Felix Fröhlich, Feb 05 2018

Extensions

Corrected a(3) and diagram for n=3. - Robert Price, Apr 02 2018

a(11)-a(85) from Robert Price, Apr 02 2018

Status

approved