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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.

%I A299207 #29 Apr 20 2018 11:39:51
%S A299207 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,
%T A299207 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,
%U A299207 1,0,8,1,2,2,1,1,1,1,1,1,1,0,3,0,7,1,1
%N 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.
%H A299207 Robert Price, <a href="/A299207/b299207.txt">Table of n, a(n) for n = 1..10000</a>
%H A299207 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ulam_spiral">Ulam spiral</a>
%H A299207 <a href="/index/Sp">Index entries for sequences related to spirals</a>
%e A299207 For n=1:
%e A299207   +------------------------+
%e A299207   | 18   17   16   15   14 |
%e A299207   |    +--------------+    |
%e A299207   | 19 |  6    5    4 | 13 |
%e A299207   |    |    +----+    |    |
%e A299207   | 20 |  7 |  2    3 | 12 |
%e A299207   |    |    +---------+    |
%e A299207   | 21 |  8    9   10   11 |
%e A299207   |    +-------------------+
%e A299207   | 22   23   24   25   26
%e A299207   +-------------------------
%e A299207 None of the four numbers located on the diagonals in NE, NW, SW or SE direction are prime, so a(1) = 0.
%e A299207 .
%e A299207 For n=2:
%e A299207   +----------------------------------+
%e A299207   | 39   38   37   36   35   34   33 |
%e A299207   |    +------------------------+    |
%e A299207   | 40 | 19   18   17   16   15 | 32 |
%e A299207   |    |    +--------------+    |    |
%e A299207   | 41 | 20 |  7    6    5 | 14 | 31 |
%e A299207   |    |    |     +---+    |    |    |
%e A299207   | 42 | 21 |  8  | 3    4 | 13 | 30 |
%e A299207   |    |    |     +--------+    |    |
%e A299207   | 43 | 22 |  9   10   11   12 | 29 |
%e A299207   |    |    +-------------------+    |
%e A299207   | 44 | 23   24   25   26   27   28 |
%e A299207   |    +-----------------------------+
%e A299207   | 45   46   47   48   49   50   51
%e A299207   +-----------------------------------
%e A299207 The encountered primes are 5 in NE direction, 7, 19, in NW direction and 11 in SE direction, so a(2) = 2.
%e A299207 .
%e A299207 For n=3:
%e A299207   +--------------------------------------------+
%e A299207   | 69   68   67   66   65   64   63   62   61 |
%e A299207   |    +----------------------------------+    |
%e A299207   | 70 | 41   40   39   38   37   36   35 | 60 |
%e A299207   |    |    +------------------------+    |    |
%e A299207   | 71 | 42 | 21   20   19   18   17 | 34 | 59 |
%e A299207   |    |    |    +--------------+    |    |    |
%e A299207   | 72 | 43 | 22 |  9    8    7 | 16 | 33 | 58 |
%e A299207   |    |    |    |    +----+    |    |    |    |
%e A299207   | 73 | 44 | 23 | 10 |  5    6 | 15 | 32 | 57 |
%e A299207   |    |    |    |    +---------+    |    |    |
%e A299207   | 74 | 45 | 24 | 11   12   13   14 | 31 | 56 |
%e A299207   |    |    |    +-------------------+    |    |
%e A299207   | 75 | 46 | 25   26   27   28   29   30 | 55 |
%e A299207   |    |    +-----------------------------+    |
%e A299207   | 76 | 47   48   49   50   51   52   53   54 |
%e A299207   |    +---------------------------------------+
%e A299207   | 77   78   79   80   81   82   83   84   85
%e A299207   +---------------------------------------------
%e A299207 The encountered primes are 7, 17 in NE direction, 11 in SW direction and 13, 29, 53 in SE direction, so a(3) = 3.
%Y A299207 Cf. A215471.
%K A299207 nonn
%O A299207 1,2
%A A299207 _Felix Fröhlich_, Feb 05 2018
%E A299207 Corrected a(3) and diagram for n=3. - _Robert Price_, Apr 02 2018
%E A299207 a(11)-a(85) from _Robert Price_, Apr 02 2018