A302244 - OEIS

%I #10 Jun 25 2018 01:10:34

%S 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,

%T 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,

%U 7,0,1,0,4,0,1,0,1,0,3,0,1,0,1,0,2,0,2

%N 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.

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

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

%H Robert Price, <a href="/A302244/b302244.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ulam_spiral">Ulam spiral</a>

%H <a href="/index/Sp">Index entries for sequences related to spirals</a>

%e For n=3:

%e +-------------------------------+

%e | 39   38  37  36  35   34   33 |

%e |    +---------------------+    |

%e | 40 | 19  18  17  16   15 | 32 |

%e |    |    +-----------+    |    |

%e | 41 | 20 | 7   6   5 | 14 | 31 |

%e |    |    |   +---+   |    |    |

%e | 42 | 21 | 8 | 3   4 | 13 | 30 |

%e |    |    |   +-------+    |    |

%e | 43 | 22 | 9  10  11   12 | 29 |

%e |    |    +----------------+    |

%e | 44 | 23  24  25  26   27   28 |

%e |    +--------------------------+

%e | 45   46  47  48  49   50   51

%e +--------------------------------

%e 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.

%Y Cf. A215471, A299207.

%K nonn

%O 0,2

%A _Robert Price_, Apr 03 2018