[ June 25, 2001 ]
29 extra Palindromic Patterns
by Hugo Sánchez from Venezuela (email)

Productos Palindrómicos 1) 111 x (1)n = 12(3)n-221 [n>=2] 2) k x 111 x (1)n = k x 12(3)n-221 [n>=2] (k x 1)(k x 2)(k x 3)n-2(k x 2)(k x 1)   [con k = {2,3}] 3) 1111 x (1)n = 123(4)n-3321 [n>=3] 4) (37)n = 37 x [(10)n-11]   [n>=1] 5) 37 x (3)1 = 111 ; 37 x (3)2 = 1221 ; 37 x (3)3 = 12321 ; 37 x (3)n = 12(3)n-221 ;   [n>=2] 6) 37 x (6)1 = 222 ; 37 x (6)2 = 2442 ; 37 x (6)3 = 24642 ; 37 x (6)n = 24(6)n-242 ;   [n>=2] 7) 37 x (9)1 = 333 ; 37 x (9)2 = 3663 ; 37 x (9)3 = 36963 ; 37 x (9)n = 36(9)n-263 8) 37 x (12)1 = 444 ; 37 x (12)n = 4(48)n-144 9) 37 x (15)1 = 555 ; 37 x (15)n + 10 = 56(06)n-15 10) 37 x (18)n + 10 = 67(27)n-16,   [n>=1] 11) 37 x (21)n + 10 = 78(48)n-17,   [n>=1] 12) 37 x (24)n + 10 = 89(69)n-18,   [n>=1] 13) 73 x (3)n + 33 = 24(3)n-242,   [n>=2] 14) 73 x (6)n + 66 = 48(6)n-284,   [n>=2] 15) 73 x (9)n = 72(9)n-227,   [n>=2] 16) 73 x (12)n + 12 = 88(48)n-28,   [n>=2] Curiosidades con el número 333667, Sez N = 333667 (primo) 17) N x (3(6)n3) = a) 1(211)221,   [n=1] b) 1(2)81,   [n=2] c) 122(332)221,   [n=3] d) 122(343)2221,   [n=4] e) 1223(4)53221,   [n=5] f) 12234455443221,   [n=6] g) 1223445(6)n-65443221,   [n>=6] 18) N x (9(6)n9) = a) 3(233)223,   [n=1] b) 3(226)2223,   [n=2] c) 32255255223,   [n=3] d) 322545545223,   [n=4] e) 3225448445223,   [n=5] f) 32254477445223,   [n=6] g) 3225447(6)n-67445223,   [n>=6] 19) N x (6(3)n6) = a) 2(122)212,   [n=1] b) 21(141)212,   [n=2] c) 21(133)2112,   [n=3] d) 211323323112,   [n=4] e) 2113225223112,   [n=5] f) 21132244223112,   [n=6] g) 2113224(3)n-64223112,   [n>=6] 20) N x (6(9)n6) = a) 2(322)232,   [n=1] b) 2(334)2332,   [n=2] c) 23(355)2332,   [n=3] d) 233565565332,   [n=4] e) 2335667665332,   [n=5] f) 23356688665332,   [n=6] g) 2335668(9)n-68665332,   [n>=6] 21) N x (3(9)n3) = a) 1(311)231,   [n=1] b) 13(323)231,   [n=2] c) 13(344)2331,   [n=3] d) 133464464331,   [n=4] e) 1334665664331,   [n=5] f) 13346677664331,   [n=6] g) 1334667(9)n-67664331,   [n>=6] 22) N x (9(3)n9) = a) 3(133)213,   [n=1] b) 31(161)213,   [n=2] c) 31(144)2113,   [n=3] d) 311424424113,   [n=4] e) 3114227224113,   [n=5] f) 31142255224113,   [n=6] g) 3114225(3)n-65224113,   [n>=6] 23) N x (9669)n = a) 3226226223,   [n=1] b) 32265488456223,   [n=2] c) 322654887788456223,   [n=3] d) 322654(8877)n-288456223,   [n>=3] 24) N x (666)n (Número dela Bestia) = a) 222222222,   [n=1] b) (2)3(4)6(2)3,   [n=2] c) (2)3(4)3(6)3(4)3(2)3,   [n=3] d) (2)3(4)3(6)6(4)3(2)3,   [n=4] e) 222444(6)3(n-2)444222,   [n>=4] 25) N x (393)n = a) 131131131,   [n=1] b) 131262(393)n-2262131,   [n>=2] 26) N x (6996)n = a) 2334334332,   [n=1] b) 23345677654332,   [n=2] c) 233456778877654332,   [n=3] d) 233456(7788)277654332,   [n=4] e) 233456(7788)n-277654332,   [n>=4] 27) N x (39693)n = a) 13244244231,   [n=1] b) 1324437667344231,   [n=2] c) 132443766(74766)n-27344231,   [n>=3] 28) N x (39393)n = a) 131144144131,   [n=1] b) 1314427557244131,   [n=2] c) 131442755737557244131,   [n=3] d) 131442(75573)n-27557244131,   [n>=3] 29) N x (36963)n = a) 12(3)721,   [n=1] b) 1233345665433321,   [n=2] c) 123334566(55566)n-25433321,   [n>=2]

Other Hugo Sánchez plates
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