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[ 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]
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