Patterns Starting With 3
Patterns that can be factored: \[[3^*03^*_7]_n={7\cdot7^{2n}-6\cdot7^{n}-1\over2}=\left(7^{n}-1\right)\left(7\cdot7^{n}+1\right)/2=\left(6\cdot[1^*_7]_n\right)\left(2\cdot[3^*4_7]_n\right)/2\] \[[3^*63^*_7]_n={7\cdot7^{2n}+6\cdot7^{n}-1\over2}=\left(7^{n}+1\right)\left(7\cdot7^{n}-1\right)/2=\left(2\cdot[3^*4_7]_{n-1}\right)\left(6\cdot[1^*_7]_{n+1}\right)/2\]
Links
> 30002: Quasi Repdigit 300..002
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> 30004: Quasi Repdigit 300..004
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> 31111: Near Repdigit 311..11
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> 31112: Quasi Repdigit 311..112
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> 31113: Depression 311..113
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> 31114: Quasi Repdigit 311..114
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> 31115: Quasi Repdigit 311..115
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> 31116: Quasi Repdigit 311..116
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> 31333: Near Repdigit 3133..33
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> 32222: Near Repdigit 322..22
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> 32226: Quasi Repdigit 322..226
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> 32333: Near Repdigit 3233..33
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> 33133: Near Repdigit Palindrome 33..33133..33
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> 33233: Near Repdigit Palindrome 33..33233..33
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> 33313: Near Repdigit 33..3313
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> 33323: Near Repdigit 33..3323
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> 33331: Near Repdigit 33..331
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> 33332: Near Repdigit 33..332
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> 33334: Near Repdigit 33..334
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> 33335: Near Repdigit 33..335
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> 33343: Near Repdigit 33..3343
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> 33353: Near Repdigit 33..3353
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> 33433: Near Repdigit Palindrome 33..33433..33
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> 33533: Near Repdigit Palindrome 33..33533..33
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> 34333: Near Repdigit 3433..33
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> 34442: Quasi Repdigit 344..442
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> 34444: Near Repdigit 344..44
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> 34446: Quasi Repdigit 344..446
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> 35333: Near Repdigit 3533..33
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> 35551: Quasi Repdigit 355..551
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> 35553: Plateau 355..553
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> 35554: Quasi Repdigit 355..554
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> 35555: Near Repdigit 355..55
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> 35556: Quasi Repdigit 355..556
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> 36662: Quasi Repdigit 366..662
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> 36664: Quasi Repdigit 366..664
(table)