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WON plate
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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]


Other Hugo Sánchez plates
won84.htm won153.htm won162.htm




A000106 Prime Curios! Prime Puzzle
Wikipedia 106 Le nombre 106














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