Hi,
a small modification of the sequence definition (effectively each
a(n) added 1, so primes are indicated by an a(n)=x=1, composites by
a number a(n)=x>1. Additionally a(n) is then in a better relation to n
than in the original definition: odd a(n) for odd(n) and even a(n) for
even n)
x the smallest natural such that
b^x = b^n (mod n)
for all 1<b<n
and then the x=a(n) for each natural arranged horizontally gives
a nice and interesting pattern of partial symmetries and broken
diagonals.
What do you think about modifying the original sequence?
Gottfried Helms
--------------------------------------------------------
|twin |
|Prime |
N |marker| x columns>12 packed
--|------|---------------------------------
2 |0
3 | 1
4 T | 2
5 | 1
6 T | 2
7 | 1
8 | 4
9 | 3
10 | 2
11 | 1
12 T | 2
13 | 1
14 | 2
15 | 3
16 | 4
17 | 1
18 T | 6
19 | 1
20 | 4
21 | 3
22 | 2
23 | 1
24 | 4
25 | 5
26 | 2
27 | 9
28 | 4
29 | 1
30 T | 2
31 | 1
32 | 8
33 | 3
34 | 2
35 | 11
36 | 6
37 | 1
38 | 2
39 | 3
40 | 4
41 | 1
42 T | 6
43 | 1
44 | 4
45 | 9
46 | 2
47 | 1
48 | 4
49 | 7
50 | 10
51 | 3
52 | 4
53 | 1
54 | 18
55 | 15
56 | 8
57 | 3
58 | 2
59 | 1
60 T | 4
61 | 1
62 | 2
63 | 3
64 | 16
65 | 5
66 | 6
67 | 1
68 | 4
69 | 3
70 | 10
71 | 1
72 T | 6
73 | 1
74 | 2
75 | 15
76 | 4
77 | 17
78 | 6
79 | 1
80 | 4
81 | 27
82 | 2
83 | 1
84 | 6
85 | 5
86 | 2
87 | 3
88 | 8
89 | 1
90 | 6
91 | 7
92 | 4
93 | 3
94 | 2
95 | 23
96 | 8
97 | 1
98 | 14
99 | 9
100 | 20
101 | 1
102 T | 6
103 | 1
104 | 8
105 | 9
106 | 2
107 | 1
108 T | 18
109 | 1
110 | 10
111 | 3
112 | 4
113 | 1
114 | 6
115 | 27
116 | 4
117 | 9
118 | 2
119 | 23
120 | 4
121 | 11
122 | 2
123 | 3
124 | 4
125 | 25
126 | 6
127 | 1
128 | 32
129 | 3
130 | 10
131 | 1
132 | 2
133 | 7
134 | 2
135 | 27
136 | 8
137 | 1
138 T | 6
139 | 1
140 | 8
141 | 3
142 | 2
143 | 23
144 | 12
145 | 5
146 | 2
147 | 21
148 | 4
149 | 1
150 T | 10
151 | 1
152 | 8
153 | 9
154 | 4
155 | 35
156 | 12
157 | 1
158 | 2
159 | 3
160 | 8
161 | 29
162 | 54
163 | 1
164 | 4
165 | 5
166 | 2
167 | 1
168 | 6
169 | 13
170 | 10
171 | 9
172 | 4
173 | 1
174 | 6
175 | 55
176 | 16
177 | 3
178 | 2
179 | 1
180 T | 12
181 | 1
182 | 2
183 | 3
184 | 8
185 | 5
186 | 6
187 | 27
188 | 4
189 | 9
190 | 10
191 | 1
192 T | 16
193 | 1
194 | 2
195 | 3
196 | 28
197 | 1
198 T | 18
199 | 1
200 | 20
201 | 3
202 | 2
203 | 35
204 | 12
205 | 5
206 | 2
207 | 9
208 | 4
209 | 29
210 | 6
211 | 1
212 | 4
213 | 3
214 | 2
215 | 47
216 | 18
217 | 7
218 | 2
219 | 3
220 | 20
221 | 29
222 | 6
223 | 1
224 | 8
225 | 45
226 | 2
227 | 1
228 T | 12
229 | 1
230 | 10
231 | 21
232 | 8
233 | 1
234 | 6
235 | 51
236 | 4
237 | 3
238 | 46
239 | 1
240 T | 4
241 | 1
242 | 22
243 | 81
244 | 4
245 | 77
246 | 6
247 | 31
248 | 8
249 | 3
250 | 50
251 | 1
252 | 6
253 | 33
254 | 2
255 | 15
256 | 64
257 | 1
258 | 6
259 | 7
260 | 8
261 | 9
262 | 2
263 | 1
264 | 4
265 | 5
266 | 14
267 | 3
268 | 4
269 | 1
270 T | 18
271 | 1
272 | 16
273 | 9
274 | 2
275 | 15
276 | 12
277 | 1
278 | 2
279 | 9
280 | 4
281 | 1
282 T | 6
283 | 1
284 | 4
285 | 33
286 | 46
287 | 47
288 | 24
289 | 17
290 | 10
291 | 3
292 | 4
293 | 1
294 | 42
295 | 63
296 | 8
297 | 27
298 | 2
299 | 35
300 | 20
301 | 7
302 | 2
303 | 3
304 | 16
305 | 5
306 | 18
307 | 1
308 | 8
309 | 3
310 | 10
311 | 1
312 T | 12
313 | 1
314 | 2
315 | 3
316 | 4
317 | 1
318 | 6
319 | 39
320 | 16
321 | 3
322 | 58
323 | 35
324 | 54
325 | 25
326 | 2
327 | 3
328 | 8
329 | 53
330 | 10
331 | 1
332 | 4
333 | 9
334 | 2
335 | 71
336 | 12
337 | 1
338 | 26
339 | 3
340 | 4
341 | 11
342 | 18
343 | 49
344 | 8
345 | 37
346 | 2
347 | 1
348 T | 12
349 | 1
350 | 50