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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A136315 A011159 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

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Last modified April 21 08:55 EDT 2019. Contains 322328 sequences. (Running on oeis4.)