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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
 1, 8, 21, 133, 278, 507, 4442, 5383, 22457, 35628, 177291, 194162, 642257, 1062108, 3351690 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. LINKS Table of n, a(n) for n=1..15. Samuel Harkness, Illustration of terms 1 through 6 EXAMPLE 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. CROSSREFS Cf. A030296, A357376. Sequence in context: A297340 A220580 A100903 * A240648 A231525 A228756 Adjacent sequences: A358717 A358718 A358719 * A358721 A358722 A358723 KEYWORD nonn,more AUTHOR Samuel Harkness, Nov 28 2022 STATUS approved

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Last modified July 16 14:47 EDT 2024. Contains 374349 sequences. (Running on oeis4.)