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

%I A358720 #11 Jan 01 2023 09:32:16
%S A358720 1,8,21,133,278,507,4442,5383,22457,35628,177291,194162,642257,
%T A358720 1062108,3351690
%N A358720 The lowest positive-integer center for a square spiral whose center lies in an n X n square of nonprimes.
%C A358720 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.
%H A358720 Samuel Harkness, <a href="/A358720/a358720_1.jpg">Illustration of terms 1 through 6</a>
%e A358720 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:
%e A358720 .
%e A358720    197  196  195  194  193  192  191  190  189
%e A358720 .
%e A358720    198  169  168  167  166  165  164  163  188
%e A358720 .                     +------------------+
%e A358720    199  170  149  148 |147  146  145  162| 187
%e A358720 .                     |                  |
%e A358720    200  171  150  137 |136  135  144  161| 186
%e A358720 .                     |                  |
%e A358720    201  172  151  138 |133  134  143  160| 185
%e A358720 .                     |                  |
%e A358720    202  173  152  139 |140  141  142  159| 184
%e A358720 .                     +------------------+
%e A358720    203  174  153  154  155  156  157  158  183
%e A358720 .
%e A358720    204  175  176  177  178  179  180  181  182
%e A358720 .
%e A358720    205  206  207  208  209  210  211  212  213
%e A358720 .
%e A358720 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.
%Y A358720 Cf. A030296, A357376.
%K A358720 nonn,more
%O A358720 1,2
%A A358720 _Samuel Harkness_, Nov 28 2022