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.

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 Sm_n 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 RSm_n 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 Pi_n 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 PRm_n 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, ...

Smarandache-type Numbers

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

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

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

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

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

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

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

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