Smarandache-type Numbers

Data for n ≤ 108 are taken from World of Numbers.
Data for n ≤ 200 are taken from M.Fleuren's lists and the pages of H.Mishima's World Integer Factorization Center.

Started: 2010-01-28     Last update: 2016-12-20

Colors: Fully factored  Prime  Semi-Prime
Note: The tables show for every n the length (L) in digits and if not completely factored the length (C) of the composite.

Here is the file containing all composite cofactors listed in the tables below.

Table 1: Factorizations of Smarandache Numbers Smn for n ≤ 200:

Pattern: 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 12345678910,...

See The On-Line Encyclopedia of Integer Sequences - A046461 for Semi-Primes.

n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C
1
1
-		 2
2
-		 3
3
-		 4
4
-		 5
5
-		 6
6
-		 7
7
-		 8
8
-		 9
9
-		 10
11
-		 11
13
-		 12
15
-		 13
17
-		 14
19
-		 15
21
-		 16
23
-		 17
25
-		 18
27
-		 19
29
-		 20
31
-
21
33
-		 22
35
-		 23
37
-		 24
39
-		 25
41
-		 26
43
-		 27
45
-		 28
47
-		 29
49
-		 30
51
-		 31
53
-		 32
55
-		 33
57
-		 34
59
-		 35
61
-		 36
63
-		 37
65
-		 38
67
-		 39
69
-		 40
71
-
41
73
-		 42
75
-		 43
77
-		 44
79
-		 45
81
-		 46
83
-		 47
85
-		 48
87
-		 49
89
-		 50
91
-		 51
93
-		 52
95
-		 53
97
-		 54
99
-		 55
101
-		 56
103
-		 57
105
-		 58
107
-		 59
109
-		 60
111
-
61
113
-		 62
115
-		 63
117
-		 64
119
-		 65
121
-		 66
123
-		 67
125
-		 68
127
-		 69
129
-		 70
131
-		 71
133
-		 72
135
-		 73
137
-		 74
139
-		 75
141
-		 76
143
-		 77
145
-		 78
147
-		 79
149
-		 80
151
-
81
153
-		 82
155
-		 83
157
-		 84
159
-		 85
161
-		 86
163
-		 87
165
-		 88
167
-		 89
169
-		 90
171
-		 91
173
-		 92
175
-		 93
177
-		 94
179
-		 95
181
-		 96
183
-		 97
185
-		 98
187
-		 99
189
-		 100
192
-
101
195
-		 102
198
-		 103
201
-		 104
204
177		 105
207
-		 106
210
-		 107
213
-		 108
216
-		 109
219
156		 110
222
-		 111
225
-		 112
228
-		 113
231
157		 114
234
162		 115
237
202		 116
240
-		 117
243
172		 118
246
174		 119
249
239		 120
252
241
121
255
-		 122
258
-		 123
261
169		 124
264
242		 125
267
224		 126
270
-		 127
273
245		 128
276
243		 129
279
277		 130
282
269		 131
285
256		 132
288
272		 133
291
272		 134
294
243		 135
297
254		 136
300
253		 137
303
258		 138
306
277		 139
309
252		 140
312
248
141
315
-		 142
318
282		 143
321
317		 144
324
-		 145
327
318		 146
330
296		 147
333
276		 148
336
-		 149
339
331		 150
342
296		 151
345
335		 152
348
-		 153
351
322		 154
354
279		 155
357
-		 156
360
354		 157
363
318		 158
366
334		 159
369
261		 160
372
292
161
375
-		 162
378
325		 163
381
330		 164
384
349		 165
387
-		 166
390
-		 167
393
389		 168
396
-		 169
399
391		 170
402
382		 171
405
347		 172
408
403		 173
411
394		 174
414
381		 175
417
403		 176
420
369		 177
423
382		 178
426
-		 179
429
423		 180
432
422
181
435
406		 182
438
429		 183
441
387		 184
444
-		 185
447
409		 186
450
425		 187
453
-		 188
456
454		 189
459
410		 190
462
-		 191
465
429		 192
468
463		 193
471
413		 194
474
373		 195
477
-		 196
480
-		 197
483
461		 198
486
453		 199
489
486		 200
492
488


Table 2: Factorizations of Reverse Smarandache Numbers RSmn for n ≤ 200:

Pattern: 1, 21, 321, 4321, 54321, 654321, 7654321, 87654321, 987654321, 10987654321,... in OEIS as A000422
More detailed information can be found at World of Numbers.

See The On-Line Encyclopedia of Integer Sequences - A176024 for Primes.

n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C
1
1
-		 2
2
-		 3
3
-		 4
4
-		 5
5
-		 6
6
-		 7
7
-		 8
8
-		 9
9
-		 10
11
-		 11
13
-		 12
15
-		 13
17
-		 14
19
-		 15
21
-		 16
23
-		 17
25
-		 18
27
-		 19
29
-		 20
31
-
21
33
-		 22
35
-		 23
37
-		 24
39
-		 25
41
-		 26
43
-		 27
45
-		 28
47
-		 29
49
-		 30
51
-		 31
53
-		 32
55
-		 33
57
-		 34
59
-		 35
61
-		 36
63
-		 37
65
-		 38
67
-		 39
69
-		 40
71
-
41
73
-		 42
75
-		 43
77
-		 44
79
-		 45
81
-		 46
83
-		 47
85
-		 48
87
-		 49
89
-		 50
91
-		 51
93
-		 52
95
-		 53
97
-		 54
99
-		 55
101
-		 56
103
-		 57
105
-		 58
107
-		 59
109
-		 60
111
-
61
113
-		 62
115
-		 63
117
-		 64
119
-		 65
121
-		 66
123
-		 67
125
-		 68
127
-		 69
129
-		 70
131
-		 71
133
-		 72
135
-		 73
137
-		 74
139
-		 75
141
-		 76
143
-		 77
145
-		 78
147
-		 79
149
-		 80
151
-
81
153
-		 82
155
-		 83
157
-		 84
159
-		 85
161
-		 86
163
-		 87
165
-		 88
167
-		 89
169
-		 90
171
-		 91
173
-		 92
175
-		 93
177
-		 94
179
-		 95
181
-		 96
183
-		 97
185
-		 98
187
-		 99
189
-		 100
192
-
101
195
-		 102
198
-		 103
201
-		 104
204
-		 105
207
-		 106
210
-		 107
213
179		 108
216
-		 109
219
-		 110
222
183		 111
225
200		 112
228
214		 113
231
219		 114
234
228		 115
237
225		 116
240
-		 117
243
-		 118
246
-		 119
249
247		 120
252
249
121
255
248		 122
258
245		 123
261
-		 124
264
259		 125
267
-		 126
270
255		 127
273
255		 128
276
263		 129
279
257		 130
282
264		 131
285
239		 132
288
-		 133
291
-		 134
294
266		 135
297
251		 136
300
300		 137
303
278		 138
306
292		 139
309
283		 140
312
289
141
315
307		 142
318
290		 143
321
-		 144
324
304		 145
327
296		 146
330
304		 147
333
321		 148
336
294		 149
339
329		 150
342
337		 151
345
335		 152
348
-		 153
351
328		 154
354
339		 155
357
347		 156
360
355		 157
363
353		 158
366
336		 159
369
340		 160
372
339
161
375
328		 162
378
361		 163
381
349		 164
384
-		 165
387
386		 166
390
344		 167
393
347		 168
396
362		 169
399
399		 170
402
-		 171
405
330		 172
408
-		 173
411
407		 174
414
-		 175
417
405		 176
420
358		 177
423
-		 178
426
-		 179
429
411		 180
432
413
181
435
409		 182
438
-		 183
441
437		 184
444
424		 185
447
432		 186
450
448		 187
453
423		 188
456
445		 189
459
433		 190
462
447		 191
465
-		 192
468
464		 193
471
462		 194
474
426		 195
477
471		 196
480
463		 197
483
440		 198
486
-		 199
489
483		 200
492
485


Table 3: Factorizations of decimal expansion of Pin for n ≤ 120:

Pattern: 3, 31, 314, 3141, 31415, 314159, 3141592, 31415926, 314159265, 3141592653,...

n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C
1
1
-		 2
2
-		 3
3
-		 4
4
-		 5
5
-		 6
6
-		 7
7
-		 8
8
-		 9
9
-		 10
10
-		 11
11
-		 12
12
-		 13
13
-		 14
14
-		 15
15
-		 16
16
-		 17
17
-		 18
18
-		 19
19
-		 20
20
-
21
21
-		 22
22
-		 23
23
-		 24
24
-		 25
25
-		 26
26
-		 27
27
-		 28
28
-		 29
29
-		 30
30
-		 31
31
-		 32
32
-		 33
33
-		 34
34
-		 35
35
-		 36
36
-		 37
37
-		 38
38
-		 39
39
-		 40
40
-
41
41
-		 42
42
-		 43
43
-		 44
44
-		 45
45
-		 46
46
-		 47
47
-		 48
48
-		 49
49
-		 50
50
-		 51
51
-		 52
52
-		 53
53
-		 54
54
-		 55
55
-		 56
56
-		 57
57
-		 58
58
-		 59
59
-		 60
60
-
61
61
-		 62
62
-		 63
63
-		 64
64
-		 65
65
-		 66
66
-		 67
67
-		 68
68
-		 69
69
-		 70
70
-		 71
71
-		 72
72
-		 73
73
-		 74
74
-		 75
75
-		 76
76
-		 77
77
-		 78
78
-		 79
79
-		 80
80
-
81
81
-		 82
82
-		 83
83
-		 84
84
-		 85
85
-		 86
86
-		 87
87
-		 88
88
-		 89
89
-		 90
90
-		 91
91
-		 92
92
-		 93
93
-		 94
94
-		 95
95
-		 96
96
-		 97
97
-		 98
98
-		 99
99
-		 100
100
-
101
101
-		 102
102
-		 103
103
-		 104
104
-		 105
105
-		 106
106
-		 107
107
-		 108
108
-		 109
109
-		 110
110
-		 111
111
-		 112
112
-		 113
113
-		 114
114
-		 115
115
-		 116
116
-		 117
117
-		 118
118
-		 119
119
-		 120
120
-
1

 2

 3

 4

 5

 6

 7

 8

 9

 0

 1

 2

 3

 4

 5

 6

 7

 8

 9

 0
Pi260 = 3561511 * P253


Table 4: Factorizations of Smarandache Numbers PRmn for n ≤ 100:

Pattern: consecutive primes 2, 23, 235, 2357, 235711, 23571113, 2357111317, ...

See The On-Line Encyclopedia of Integer Sequences - A019518.
See The On-Line Encyclopedia of Integer Sequences - A069151 for primes.

n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C		 n
L
C
1
1
-		 2
2
-		 3
3
-		 4
4
-		 5
6
-		 6
8
-		 7
10
-		 8
12
-		 9
14
-		 10
16
-		 11
18
-		 12
20
-		 13
22
-		 14
24
-		 15
26
-		 16
28
-		 17
30
-		 18
32
-		 19
34
-		 20
36
-
21
38
-		 22
40
-		 23
42
-		 24
44
-		 25
46
-		 26
49
-		 27
52
-		 28
55
-		 29
58
-		 30
61
-		 31
64
-		 32
67
-		 33
70
-		 34
73
-		 35
76
-		 36
79
-		 37
82
-		 38
85
-		 39
88
-		 40
91
-
41
94
-		 42
97
-		 43
100
-		 44
103
-		 45
106
-		 46
109
-		 47
112
-		 48
115
-		 49
118
-		 50
121
-		 51
124
-		 52
127
-		 53
130
-		 54
133
-		 55
136
-		 56
139
-		 57
142
-		 58
145
-		 59
148
-		 60
151
-
61
154
-		 62
157
-		 63
160
-		 64
163
-		 65
166
-		 66
169
-		 67
172
-		 68
175
-		 69
178
-		 70
181
164		 71
184
164		 72
187
-		 73
190
-		 74
193
-		 75
196
177		 76
199
167		 77
202
157		 78
205
200		 79
208
-		 80
211
171
81
214
-		 82
217
202		 83
220
-		 84
223
-		 85
226
-		 86
229
161		 87
232
-		 88
235
189		 89
238
160		 90
241
210		 91
244
206		 92
247
234		 93
250
227		 94
253
241		 95
256
189		 96
259
-		 97
262
228		 98
265
-		 99
268
239		 100
271
239
1

 2

 3

 4

 5

 6

 7

 8

 9

 0

 1

 2

 3

 4

 5

 6

 7

 8

 9

 0

Prime for n = 1, 2, 4, 128, 174, 342, 435, 1429 (n < 10400), see The On-Line Encyclopedia of Integer Sequences - A046035 and A046284.



Others:
Base 3: 1, 12, 1210, 121011, 12101112, 1210111220, ... or in decimal 1, 5, 48, 436, 3929, 35367, 318310, 2864798, ...
Base 4: 1, 12, 123, 12310, 1231011, 123101112, 12310111213, 1231011121320, ... or in decimal 1, 6, 27, 436, 6981, 111702, 1787239, 28595832, 457533321, ...
Base 5: 1, 12, 123, 1234, 123410, 12341011, 1234101112, 123410111213, ... or in decimal 1, 7, 38, 194, 4855, 121381, 3034532, 75863308, 1896582709, ...
Base 6: 1, 12, 123, 1234, 12345, 1234510, 123451011, 12345101112, 1234510111213, ... or in decimal 1, 8, 51, 310, 1865, 67146, 2417263, 87021476, ...
Base 7: 1, 12, 123, 1234, 12345, 123456, 12345610, 1234561011, 123456101112, ... or in decimal 1, 9, 66, 466, 3267, 22875, 1120882, 54923226, ...
Base 8: 1, 12, 123, 1234, 12345, 123456, 1234567, 123456710, 12345671011, ... or in decimal 1, 10, 83, 668, 5349, 42798, 342391, 21913032, 1402434057, ...
Base 9: 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 1234567810, ... or in decimal 1, 11, 102, 922, 8303, 74733, 672604, 6053444, 490328973, ...
Symetric: 1,11,121,1221,12321,123321,1234321,12344321,123454321,1234554321, ...
Mirror: 1, 212, 32123, 4321234, 543212345, 65432123456, ...
Permutation: 12, 1342, 135642, 13578642, 13579108642, 135791112108642, 1357911131412108642, ...
Permutation/2: 6, 671, 67821, 6789321, 6789554321, 67895556054321, 678955565706054321, 6789555657580706054321, ...
Antisymmetric: 11, 1212, 123123, 12341234, 1234512345, 123456123456, 12345671234567, ...
Odd: 1, 13, 135, 1357, 13579, 1357911, 135791113, 13579111315, ...
Even: 2, 24, 246, 2468, 246810, 24681012, 2468101214, ...
Even/2: 1, 12, 123, 1234, 123405, 12340506, 1234050607, ...
Square: 1, 14, 149, 14916, 1491625, 149162536, 14916253649, ...
Cubic: 1, 18, 1827, 182764, 182764125, 182764125216, ...
Fibonacci: 1, 11, 112, 1123, 11235, 112358, 11235813, ...
Lucas: 2, 21, 213, 2134, 21347, 2134711, 213471118, ...