tables > nrr > 6

Base 6

Patterns that can be factored: \[[1^*01^*_6]_n={6\cdot6^{2n}-5\cdot6^{n}-1\over5}=\left(6^{n}-1\right)\left(6\cdot6^{n}+1\right)/5=\left(5\cdot[1^*_6]_n\right)\left([10^*1_6]_n\right)/5\] \[[1^*21^*_6]_n={6\cdot6^{2n}+5\cdot6^{n}-1\over5}=\left(6^{n}+1\right)\left(6\cdot6^{n}-1\right)/5=\left([10^*1_6]_{n-1}\right)\left(5\cdot[1^*_6]_{n+1}\right)/5\] \[[2^*02^*_6]_n=2\cdot{6\cdot6^{2n}-5\cdot6^{n}-1\over5}=2\cdot\left(6^{n}-1\right)\left(6\cdot6^{n}+1\right)/5=2\cdot\left(5\cdot[1^*_6]_n\right)\left([10^*1_6]_n\right)/5\] \[[2^*42^*_6]_n=2\cdot{6\cdot6^{2n}+5\cdot6^{n}-1\over5}=2\cdot\left(6^{n}+1\right)\left(6\cdot6^{n}-1\right)/5=2\cdot\left([10^*1_6]_{n-1}\right)\left(5\cdot[1^*_6]_{n+1}\right)/5\] \[[2^*12^*_6]_n={12\cdot6^{2n}-5\cdot6^{n}-2\over5}=\left(3\cdot6^{n}-2\right)\left(4\cdot6^{n}+1\right)/5=\left([5^*2_6]_n/2\right)\left(5\cdot[4^*5_6]_{n-1}\right)/5\] \[[2^*32^*_6]_n={12\cdot6^{2n}+5\cdot6^{n}-2\over5}=\left(3\cdot6^{n}+2\right)\left(4\cdot6^{n}-1\right)/5=\left(10\cdot[14^*5_6]_{n-2}\right)\left([35^*_6]_n\right)/5\] \[[3^*03^*_6]_n=3\cdot{6\cdot6^{2n}-5\cdot6^{n}-1\over5}=3\cdot\left(6^{n}-1\right)\left(6\cdot6^{n}+1\right)/5=3\cdot\left(5\cdot[1^*_6]_n\right)\left([10^*1_6]_n\right)/5\] \[[4^*04^*_6]_n=4\cdot{6\cdot6^{2n}-5\cdot6^{n}-1\over5}=4\cdot\left(6^{n}-1\right)\left(6\cdot6^{n}+1\right)/5=4\cdot\left(5\cdot[1^*_6]_n\right)\left([10^*1_6]_n\right)/5\] \[[4^*24^*_6]_n=2\cdot{12\cdot6^{2n}-5\cdot6^{n}-2\over5}=2\cdot\left(3\cdot6^{n}-2\right)\left(4\cdot6^{n}+1\right)/5=2\cdot\left([5^*2_6]_n/2\right)\left(5\cdot[4^*5_6]_{n-1}\right)/5\] \[[5^*05^*_6]_n=6\cdot6^{2n}-5\cdot6^{n}-1=\left(6^{n}-1\right)\left(6\cdot6^{n}+1\right)=\left(5\cdot[1^*_6]_n\right)\left([10^*1_6]_n\right)\] \[[5^*45^*_6]_n=6\cdot6^{2n}-6^{n}-1=\left(2\cdot6^{n}-1\right)\left(3\cdot6^{n}+1\right)=\left([15^*_6]_n\right)\left([30^*1_6]_{n-1}\right)\]

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> 10001: Depression 100..001 (table) > 10005: Quasi Repdigit 100..005 (table) > 10111: Near Repdigit 1011..11 (table) > 11101: Near Repdigit 11..1101 (table) > 11111: Repunit 11..11 (table) > 11115: Near Repdigit 11..115 (table) > 11121: Near Repdigit 11..1121 (table) > 11131: Near Repdigit 11..1131 (table) > 11141: Near Repdigit 11..1141 (table) > 11151: Near Repdigit 11..1151 (table) > 11311: Near Repdigit Palindrome 11..11311..11 (table) > 11411: Near Repdigit Palindrome 11..11411..11 (table) > 11511: Near Repdigit Palindrome 11..11511..11 (table) > 12111: Near Repdigit 1211..11 (table) > 12224: Quasi Repdigit 122..224 (table) > 12225: Quasi Repdigit 122..225 (table) > 13111: Near Repdigit 1311..11 (table) > 13331: Plateau 133..331 (table) > 13335: Quasi Repdigit 133..335 (table) > 14111: Near Repdigit 1411..11 (table) > 14441: Plateau 144..441 (table) > 14444: Near Repdigit 144..44 (table) > 14445: Quasi Repdigit 144..445 (table) > 15111: Near Repdigit 1511..11 (table) > 15551: Plateau 155..551 (table) > 15555: Near Repdigit 155..55 (table) > 20001: Quasi Repdigit 200..001 (table) > 20005: Quasi Repdigit 200..005 (table) > 21111: Near Repdigit 211..11 (table) > 21112: Depression 211..112 (table) > 21113: Quasi Repdigit 211..113 (table) > 21114: Quasi Repdigit 211..114 (table) > 21115: Quasi Repdigit 211..115 (table) > 21222: Near Repdigit 2122..22 (table) > 22221: Near Repdigit 22..221 (table) > 22225: Near Repdigit 22..225 (table) > 22252: Near Repdigit 22..2252 (table) > 22522: Near Repdigit Palindrome 22..22522..22 (table) > 23222: Near Repdigit 2322..22 (table) > 23332: Plateau 233..332 (table) > 23334: Quasi Repdigit 233..334 (table) > 23335: Quasi Repdigit 233..335 (table) > 24441: Quasi Repdigit 244..441 (table) > 24445: Quasi Repdigit 244..445 (table) > 25551: Quasi Repdigit 255..551 (table) > 25552: Plateau 255..552 (table) > 25555: Near Repdigit 255..55 (table) > 30001: Quasi Repdigit 300..001 (table) > 30004: Quasi Repdigit 300..004 (table) > 30005: Quasi Repdigit 300..005 (table) > 31111: Near Repdigit 311..11 (table) > 31113: Depression 311..113 (table) > 31115: Quasi Repdigit 311..115 (table) > 31333: Near Repdigit 3133..33 (table) > 32221: Quasi Repdigit 322..221 (table) > 32223: Depression 322..223 (table) > 32224: Quasi Repdigit 322..224 (table) > 32225: Quasi Repdigit 322..225 (table) > 32333: Near Repdigit 3233..33 (table) > 33133: Near Repdigit Palindrome 33..33133..33 (table) > 33233: Near Repdigit Palindrome 33..33233..33 (table) > 33323: Near Repdigit 33..3323 (table) > 33331: Near Repdigit 33..331 (table) > 33335: Near Repdigit 33..335 (table) > 33433: Near Repdigit Palindrome 33..33433..33 (table) > 33533: Near Repdigit Palindrome 33..33533..33 (table) > 34333: Near Repdigit 3433..33 (table) > 34442: Quasi Repdigit 344..442 (table) > 34443: Plateau 344..443 (table) > 34444: Near Repdigit 344..44 (table) > 34445: Quasi Repdigit 344..445 (table) > 35333: Near Repdigit 3533..33 (table) > 35551: Quasi Repdigit 355..551 (table) > 35553: Plateau 355..553 (table) > 35555: Near Repdigit 355..55 (table) > 40003: Quasi Repdigit 400..003 (table) > 40005: Quasi Repdigit 400..005 (table) > 41111: Near Repdigit 411..11 (table) > 41115: Quasi Repdigit 411..115 (table) > 41444: Near Repdigit 4144..44 (table) > 42221: Quasi Repdigit 422..221 (table) > 42225: Quasi Repdigit 422..225 (table) > 43331: Quasi Repdigit 433..331 (table) > 43332: Quasi Repdigit 433..332 (table) > 43334: Depression 433..334 (table) > 43335: Quasi Repdigit 433..335 (table) > 43444: Near Repdigit 4344..44 (table) > 44144: Near Repdigit Palindrome 44..44144..44 (table) > 44344: Near Repdigit Palindrome 44..44344..44 (table) > 44414: Near Repdigit 44..4414 (table) > 44434: Near Repdigit 44..4434 (table) > 44441: Near Repdigit 44..441 (table) > 44445: Near Repdigit 44..445 (table) > 44544: Near Repdigit Palindrome 44..44544..44 (table) > 45444: Near Repdigit 4544..44 (table) > 45552: Quasi Repdigit 455..552 (table) > 45553: Quasi Repdigit 455..553 (table) > 45554: Plateau 455..554 (table) > 45555: Near Repdigit 455..55 (table) > 50001: Quasi Repdigit 500..001 (table) > 50002: Quasi Repdigit 500..002 (table) > 50003: Quasi Repdigit 500..003 (table) > 50004: Quasi Repdigit 500..004 (table) > 51111: Near Repdigit 511..11 (table) > 51113: Quasi Repdigit 511..113 (table) > 51115: Depression 511..115 (table) > 51555: Near Repdigit 5155..55 (table) > 52221: Quasi Repdigit 522..221 (table) > 52224: Quasi Repdigit 522..224 (table) > 52225: Depression 522..225 (table) > 52555: Near Repdigit 5255..55 (table) > 53331: Quasi Repdigit 533..331 (table) > 53555: Near Repdigit 5355..55 (table) > 54441: Quasi Repdigit 544..441 (table) > 54442: Quasi Repdigit 544..442 (table) > 54443: Quasi Repdigit 544..443 (table) > 54444: Near Repdigit 544..44 (table) > 54445: Depression 544..445 (table) > 54555: Near Repdigit 5455..55 (table) > 55155: Near Repdigit Palindrome 55..55155..55 (table) > 55255: Near Repdigit Palindrome 55..55255..55 (table) > 55355: Near Repdigit Palindrome 55..55355..55 (table) > 55515: Near Repdigit 55..5515 (table) > 55525: Near Repdigit 55..5525 (table) > 55535: Near Repdigit 55..5535 (table) > 55545: Near Repdigit 55..5545 (table) > 55551: Near Repdigit 55..551 (table) > 55552: Near Repdigit 55..552 (table)