Some known self-stuffable primitive roots Using Lars' example of concatenation to arrive at 21021021021021021021 as a self-stuffable primitive root, I have been able to find similar concatenations that show any of the digits 1-9 may be the ending digit of such a number. # digits M L m 2 22 4 0 3 126 9 0 20 21 3 3 52 23 5 5 59 32004 9 3 94 1035 9 5 114 100503 9 6 137 12026 11 6 202 2115 9 11 204 111035 11 9 266 132004 10 13 355 308 11 16 436 2205 9 24 490 220115 11 22 525 21205 10 26 576 4009 13 22 603 303 6 50 605 11211 6 50 648 1303 7 46 704 1213 7 50 816 104013 9 45 867 219 12 36 873 14002 7 62 888 302013 9 49 1072 123007 13 41 1109 31101 6 92 1111 10402 7 79 1286 103204 10 64 1304 1121 5 130 1305 13105 10 65 1370 105005 11 62 1504 3011 5 150 1566 100149 15 52 2021 12209 14 72 2137 21208 13 82 2205 22105 10 110 2219 40014 9 123 2502 110407 13 96 2683 50008 13 103 2800 510005 11 127 3105 31105 10 155 3246 120213 9 180 3562 100058 14 127 4206 101044 10 210 4476 121119 15 149 4822 101138 14 172 5002 3013 7 357 5258 200317 13 202 5306 1127 11 241 5396 231005 11 245 5495 22014 9 305 5550 211023 9 308 5816 211201 7 415 6053 12113 8 378 6246 150004 10 312 6670 200131 7 476 6672 200315 11 303 6894 110406 12 287 6900 221013 9 383 8456 220207 13 325 8673 22106 11 394 9176 110131 7 655 9201 10046 11 418 9442 131018 14 337 10056 230109 15 335 10914 131013 9 606 11220 202023 9 623 11382 140013 9 632 12088 101131 7 863 12106 121115 11 550 12126 2207 11 551 12746 204004 10 637 13604 312007 13 523 13798 110402 8 862 13916 105007 13 535 13954 330005 11 634 14044 2209 13 540 14622 100328 14 522 14640 410013 9 813 15537 11306 11 706 15868 101045 11 721 16440 400205 11 747 16489 20308 13 634 16998 102033 9 944 19036 121205 11 865 19340 140011 7 1381 19608 3019 13 754 19773 11302 7 1412 20334 122011 7 1452 20346 122103 9 1130 21033 12022 7 1502 22026 4007 11 1001 24726 300039 15 824 25046 200404 10 1252 25538 120127 13 982 26032 150005 11 1183 26164 310115 11 1189 26242 420008 14 937 27746 222004 10 1387 28818 132008 14 1029 28874 231001 7 2062 29196 210309 15 973 29882 222001 7 2134 30568 131011 7 2183 33486 410109 15 1116 33846 203103 9 1880 33956 600001 7 2425 34876 222005 11 1585 35911 22108 13 1381 36186 240004 10 1809 36680 100055 11 1667 37692 240005 11 1713 38770 141005 11 1762 40002 320103 9 2222 40926 311109 15 1364 41497 30206 11 1886 41809 50002 7 2986 44006 120035 11 2000 45422 210218 14 1622 45869 13109 14 1638 47200 310201 7 3371 48736 310205 11 2215 50246 402004 10 2512 51504 103023 9 2861 51828 311103 9 2879 52494 420006 12 2187 52548 210213 9 2919 56005 32009 14 2000 59338 330007 13 2282 60144 120303 9 3341 63255 23006 11 2875 64576 411005 11 2935 65004 130023 9 3611 66968 121201 7 4783 70173 40102 7 5012 70496 141001 7 5035 71526 200319 15 2384 74444 102037 13 2863 77369 22109 14 2763 79326 201039 15 2644 91896 110319 15 3063 95738 103117 13 3682 98678 510001 7 7048 100104 200223 9 5561 100644 201303 9 5591 102500 410011 7 7321 105089 30029 14 3753 106044 212103 9 5891 107828 301117 13 4147 108396 130119 15 3613 110225 40106 11 5010 110248 100235 11 5011 112228 102035 11 5101 116108 210121 7 8293 119996 240007 13 4615 121336 110315 11 5515 122506 140018 14 4375 126636 101319 15 4221 128226 310119 15 4274 138786 111039 15 4626 164996 330001 7 11785 178870 102218 14 6388 197770 113018 14 7063 199248 400023 9 11069 222316 202115 11 10105 229158 420005 11 10416 232216 211115 11 10555 233226 300127 13 8970 251256 100509 15 8375 260256 104109 15 8675 263886 211119 15 8796 302556 121029 15 10085 331216 301115 11 15055 350230 200138 14 12508 350256 140109 15 11675 351434 100411 7 25102 373344 320011 7 26667 389234 111211 7 27802 395534 113011 7 28252 500974 310207 13 19268 503256 201309 15 16775 505056 202029 15 16835 544270 311018 14 19438 656506 303007 13 25250 695506 321007 13 26750 704234 201211 7 50302 710534 203011 7 50752 722312 111127 13 27781 729332 112207 13 28051 750756 300309 15 25025 752106 301119 15 25070 752556 301029 15 25085 755256 302109 15 25175 800256 320109 15 26675 867106 400207 13 33350 1105006 510007 13 42500 1250256 500109 15 41675 1302632 200407 13 50101 1326032 204007 13 51001 1365812 210127 13 52531 1443032 222007 13 55501 2671532 411007 13 102751 The first two lines represent the familiar 22 and 126 original examples. The third line represents the one Lars found. To my knowledge the rest are new. The corresponding self-stuffable primitive root can be computed from the parameters in the table using the following formula: sspr_M_m = M* Sum(10^(k*L),{k,0,2m}) where L is the sum of digits of M. These primitive solutions may be extended to imprimitive solutions by similarly concatenating any odd number of copies of a primitive solution. There may be other solutions missing in this table with larger values of M that result in lower values of m.