A357376 The lowest number on Ulam Spiral for which all numbers in the square which is centered at a(n) and spans n-1 spaces in each cardinal direction are nonprime.

1, 26, 1016, 5136, 39639, 203100, 2729736, 32264250, 42119062, 1065799391, 12444190246

Offset: 1

Author

Samuel Harkness, Sep 26 2022

Keywords

• nonn
• more

Comments

The n-th term creates a (2*n-1) X (2*n-1) square centered at a(n).

Examples

			For n=2, test squares with 1 layer of numbers around the center number until a square is enclosed with only nonprimes.
.
   65   64   63   62   61   60   59   58   57
.
   66   37   36   35   34   33   32   31   56
.
   67   38   17   16   15   14   13   30   55
.
   68   39   18    5    4    3   12   29   54
.
   69   40   19    6    1    2   11   28   53
.                              +--------------+
   70   41   20    7    8    9 | 10   27   52 |
.                              |              |
   71   42   21   22   23   24 | 25   26   51 |
.                              |              |
   72   43   44   45   46   47 | 48   49   50 |
.                              +--------------+
   73   74   75   76   77   78   79   80   81
.
The first number tested, 1, does not work because 2, 3, 5 and 7 are in the 1-layered square and are prime. The first square that works is 26 because 10, 27, 52, 25, 26, 51, 48, 49, and 50 are all nonprime.
		

Links

• Samuel Harkness, Illustration of terms 1 through 4
• Rémy Sigrist, C++ program

Crossrefs

Cf. A000040, A115258, A136626, A225073.

Extensions

a(8)-a(11) from Rémy Sigrist, Sep 27 2022