Patterns Starting With 5
Patterns that can be factored: \[[5^*05^*_7]_n=5\cdot{7\cdot7^{2n}-6\cdot7^{n}-1\over6}=5\cdot\left(7^{n}-1\right)\left(7\cdot7^{n}+1\right)/6=5\cdot\left(6\cdot[1^*_7]_n\right)\left(2\cdot[3^*4_7]_n\right)/6\] \[[5^*25^*_7]_n={35\cdot7^{2n}-18\cdot7^{n}-5\over6}=\left(5\cdot7^{n}+1\right)\left(7\cdot7^{n}-5\right)/6=\left(6\cdot[5^*6_7]_{n-1}\right)\left(2\cdot[3^*1_7]_n\right)/6\]
Links
> 50002: Quasi Repdigit 500..002
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> 50006: Quasi Repdigit 500..006
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> 51111: Near Repdigit 511..11
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> 51112: Quasi Repdigit 511..112
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> 51113: Quasi Repdigit 511..113
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> 51114: Quasi Repdigit 511..114
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> 51115: Depression 511..115
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> 51116: Quasi Repdigit 511..116
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> 51555: Near Repdigit 5155..55
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> 52222: Near Repdigit 522..22
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> 52224: Quasi Repdigit 522..224
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> 52226: Quasi Repdigit 522..226
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> 52555: Near Repdigit 5255..55
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> 53332: Quasi Repdigit 533..332
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> 53333: Near Repdigit 533..33
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> 53335: Depression 533..335
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> 53336: Quasi Repdigit 533..336
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> 53555: Near Repdigit 5355..55
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> 54442: Quasi Repdigit 544..442
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> 54444: Near Repdigit 544..44
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> 54446: Quasi Repdigit 544..446
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> 54555: Near Repdigit 5455..55
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> 55155: Near Repdigit Palindrome 55..55155..55
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> 55355: Near Repdigit Palindrome 55..55355..55
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> 55455: Near Repdigit Palindrome 55..55455..55
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> 55515: Near Repdigit 55..5515
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> 55525: Near Repdigit 55..5525
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> 55535: Near Repdigit 55..5535
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> 55545: Near Repdigit 55..5545
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> 55551: Near Repdigit 55..551
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> 55552: Near Repdigit 55..552
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> 55553: Near Repdigit 55..553
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> 55554: Near Repdigit 55..554
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> 55556: Near Repdigit 55..556
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> 55565: Near Repdigit 55..5565
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> 55655: Near Repdigit Palindrome 55..55655..55
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> 56555: Near Repdigit 5655..55
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> 56662: Quasi Repdigit 566..662
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> 56666: Near Repdigit 566..66
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