A358720 The lowest positive-integer center for a square spiral whose center lies in an n X n square of nonprimes.

1, 8, 21, 133, 278, 507, 4442, 5383, 22457, 35628, 177291, 194162, 642257, 1062108, 3351690

Offset: 1

Author

Samuel Harkness, Nov 28 2022

Keywords

• nonn
• more

Comments

a(n) <= A030296(n^2). A run of n^2 composite numbers guarantees a square spiral centered at the start of the run will lie in an n X n square of nonprimes.

Examples

			For n=4, test square spirals centered at each positive integer until one is found which lies in a 4 X 4 square of nonprimes. Square spirals centered at 1..132 do not work, then for 133 the following square spiral is produced:
.
   197  196  195  194  193  192  191  190  189
.
   198  169  168  167  166  165  164  163  188
.                     +------------------+
   199  170  149  148 |147  146  145  162| 187
.                     |                  |
   200  171  150  137 |136  135  144  161| 186
.                     |                  |
   201  172  151  138 |133  134  143  160| 185
.                     |                  |
   202  173  152  139 |140  141  142  159| 184
.                     +------------------+
   203  174  153  154  155  156  157  158  183
.
   204  175  176  177  178  179  180  181  182
.
   205  206  207  208  209  210  211  212  213
.
Note that 147, 146, 145, 162, 136, 135, 144, 161, 133, 134, 143, 160, 140, 141, 142, and 159 are all nonprime, so the square spiral centered at 133 works.
		

Links

• Samuel Harkness, Illustration of terms 1 through 6

Crossrefs

Cf. A030296, A357376.