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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. 1

%I #11 Jan 01 2023 09:32:16

%S 1,8,21,133,278,507,4442,5383,22457,35628,177291,194162,642257,

%T 1062108,3351690

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

%C 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 Samuel Harkness, <a href="/A358720/a358720_1.jpg">Illustration of terms 1 through 6</a>

%e 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 .

%e 197 196 195 194 193 192 191 190 189

%e .

%e 198 169 168 167 166 165 164 163 188

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

%e 199 170 149 148 |147 146 145 162| 187

%e . | |

%e 200 171 150 137 |136 135 144 161| 186

%e . | |

%e 201 172 151 138 |133 134 143 160| 185

%e . | |

%e 202 173 152 139 |140 141 142 159| 184

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

%e 203 174 153 154 155 156 157 158 183

%e .

%e 204 175 176 177 178 179 180 181 182

%e .

%e 205 206 207 208 209 210 211 212 213

%e .

%e 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 Cf. A030296, A357376.

%K nonn,more

%O 1,2

%A _Samuel Harkness_, Nov 28 2022

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Last modified August 13 21:35 EDT 2024. Contains 375144 sequences. (Running on oeis4.)