Find all Palindromes between 1 and 10,000 in multiple bases

 

# Find all numbers between 1 to 10,000 which are palindromes in more than one base

def digit_to_char(digit):
    if digit < 10:
        return str(digit)
    return chr(ord('a') + digit - 10)

def str_base(number,base):
    if number < 0:
        return '-' + str_base(-number, base)
    (d, m) = divmod(number, base)
    if d > 0:
        return str_base(d, base) + digit_to_char(m)
    return digit_to_char(m)



for S in range(1, 10001):
    n = 0
    S += 1
    palindromeCount = 0
    msg = ""
    for B in range(2,11):
        inBaseB = str_base(S, B)
        if inBaseB == inBaseB[::-1]:
            msg += " base " + str(B) + ": " + inBaseB + ";"
            palindromeCount += 1
    if palindromeCount >= 2:
        print(str(S) + "(" + msg + " )")
        
2( base 3: 2; base 4: 2; base 5: 2; base 6: 2; base 7: 2; base 8: 2; base 9: 2; base 10: 2; )
3( base 2: 11; base 4: 3; base 5: 3; base 6: 3; base 7: 3; base 8: 3; base 9: 3; base 10: 3; )
4( base 3: 11; base 5: 4; base 6: 4; base 7: 4; base 8: 4; base 9: 4; base 10: 4; )
5( base 2: 101; base 4: 11; base 6: 5; base 7: 5; base 8: 5; base 9: 5; base 10: 5; )
6( base 5: 11; base 7: 6; base 8: 6; base 9: 6; base 10: 6; )
7( base 2: 111; base 6: 11; base 8: 7; base 9: 7; base 10: 7; )
8( base 3: 22; base 7: 11; base 9: 8; base 10: 8; )
9( base 2: 1001; base 8: 11; base 10: 9; )
10( base 3: 101; base 4: 22; base 9: 11; )
15( base 2: 1111; base 4: 33; )
16( base 3: 121; base 7: 22; )
17( base 2: 10001; base 4: 101; )
18( base 5: 33; base 8: 22; )
20( base 3: 202; base 9: 22; )
21( base 2: 10101; base 4: 111; base 6: 33; )
24( base 5: 44; base 7: 33; )
26( base 3: 222; base 5: 101; )
27( base 2: 11011; base 8: 33; )
28( base 3: 1001; base 6: 44; )
31( base 2: 11111; base 5: 111; )
33( base 2: 100001; base 10: 33; )
36( base 5: 121; base 8: 44; )
40( base 3: 1111; base 7: 55; base 9: 44; )
45( base 2: 101101; base 8: 55; )
46( base 4: 232; base 5: 141; )
50( base 7: 101; base 9: 55; )
51( base 2: 110011; base 4: 303; )
52( base 3: 1221; base 5: 202; )
55( base 4: 313; base 6: 131; base 10: 55; )
57( base 5: 212; base 7: 111; )
63( base 2: 111111; base 4: 333; base 8: 77; )
65( base 2: 1000001; base 4: 1001; base 8: 101; )
67( base 5: 232; base 6: 151; )
73( base 2: 1001001; base 8: 111; )
78( base 5: 303; base 7: 141; )
80( base 3: 2222; base 6: 212; base 9: 88; )
82( base 3: 10001; base 9: 101; )
85( base 2: 1010101; base 4: 1111; base 7: 151; )
88( base 5: 323; base 10: 88; )
91( base 3: 10101; base 9: 111; )
92( base 6: 232; base 7: 161; )
93( base 2: 1011101; base 5: 333; )
98( base 5: 343; base 6: 242; )
99( base 2: 1100011; base 10: 99; )
100( base 3: 10201; base 7: 202; base 9: 121; )
104( base 5: 404; base 6: 252; )
105( base 4: 1221; base 8: 151; )
107( base 2: 1101011; base 7: 212; )
109( base 5: 414; base 9: 131; )
111( base 6: 303; base 10: 111; )
114( base 5: 424; base 7: 222; )
119( base 2: 1110111; base 5: 434; )
121( base 3: 11111; base 7: 232; base 8: 171; base 10: 121; )
127( base 2: 1111111; base 9: 151; )
129( base 2: 10000001; base 6: 333; )
130( base 3: 11211; base 4: 2002; base 8: 202; )
135( base 6: 343; base 7: 252; )
141( base 6: 353; base 10: 141; )
142( base 3: 12021; base 7: 262; )
150( base 4: 2112; base 7: 303; )
151( base 3: 12121; base 10: 151; )
154( base 6: 414; base 8: 232; base 9: 181; )
160( base 3: 12221; base 6: 424; )
164( base 3: 20002; base 7: 323; base 9: 202; )
170( base 4: 2222; base 8: 252; )
171( base 7: 333; base 10: 171; )
173( base 3: 20102; base 9: 212; )
178( base 6: 454; base 7: 343; base 8: 262; )
182( base 3: 20202; base 9: 222; )
185( base 6: 505; base 7: 353; )
186( base 5: 1221; base 8: 272; )
191( base 6: 515; base 9: 232; base 10: 191; )
195( base 2: 11000011; base 4: 3003; base 8: 303; )
200( base 7: 404; base 9: 242; )
203( base 3: 21112; base 6: 535; base 8: 313; )
209( base 6: 545; base 9: 252; )
212( base 3: 21212; base 10: 212; )
215( base 4: 3113; base 6: 555; )
219( base 2: 11011011; base 8: 333; )
227( base 8: 343; base 9: 272; )
235( base 4: 3223; base 7: 454; base 8: 353; )
242( base 3: 22222; base 7: 464; base 10: 242; )
246( base 5: 1441; base 9: 303; )
252( base 5: 2002; base 10: 252; )
255( base 2: 11111111; base 4: 3333; base 9: 313; )
257( base 2: 100000001; base 4: 10001; base 7: 515; )
264( base 7: 525; base 9: 323; )
273( base 2: 100010001; base 4: 10101; base 9: 333; )
282( base 5: 2112; base 9: 343; base 10: 282; )
292( base 7: 565; base 8: 444; base 10: 292; )
300( base 7: 606; base 8: 454; base 9: 363; )
313( base 2: 100111001; base 10: 313; )
316( base 3: 102201; base 8: 474; )
325( base 2: 101000101; base 4: 11011; base 8: 505; )
328( base 3: 110011; base 7: 646; base 9: 404; )
333( base 8: 515; base 10: 333; )
341( base 2: 101010101; base 4: 11111; base 8: 525; )
342( base 5: 2332; base 7: 666; )
343( base 6: 1331; base 10: 343; )
357( base 4: 11211; base 8: 545; )
364( base 3: 111111; base 9: 444; )
365( base 2: 101101101; base 8: 555; )
373( base 4: 11311; base 8: 565; base 9: 454; base 10: 373; )
381( base 2: 101111101; base 8: 575; )
393( base 4: 12021; base 10: 393; )
400( base 3: 112211; base 7: 1111; base 9: 484; )
414( base 8: 636; base 10: 414; )
427( base 2: 110101011; base 6: 1551; )
434( base 6: 2002; base 10: 434; )
438( base 5: 3223; base 8: 666; )
446( base 8: 676; base 9: 545; )
455( base 2: 111000111; base 8: 707; base 9: 555; )
464( base 9: 565; base 10: 464; )
471( base 2: 111010111; base 8: 727; )
484( base 3: 122221; base 10: 484; )
495( base 2: 111101111; base 8: 757; )
511( base 2: 111111111; base 8: 777; )
513( base 2: 1000000001; base 8: 1001; )
546( base 4: 20202; base 9: 666; )
555( base 9: 676; base 10: 555; )
560( base 3: 202202; base 6: 2332; )
564( base 5: 4224; base 9: 686; )
585( base 2: 1001001001; base 8: 1111; base 10: 585; )
624( base 5: 4444; base 7: 1551; )
626( base 5: 10001; base 10: 626; )
644( base 3: 212212; base 6: 2552; )
646( base 9: 787; base 10: 646; )
651( base 5: 10101; base 6: 3003; )
656( base 3: 220022; base 9: 808; base 10: 656; )
666( base 4: 22122; base 10: 666; )
676( base 5: 10201; base 10: 676; )
692( base 3: 221122; base 9: 848; )
693( base 2: 1010110101; base 6: 3113; )
701( base 5: 10301; base 9: 858; )
717( base 2: 1011001101; base 10: 717; )
728( base 3: 222222; base 9: 888; )
730( base 3: 1000001; base 9: 1001; )
757( base 3: 1001001; base 10: 757; )
771( base 2: 1100000011; base 4: 30003; )
777( base 6: 3333; base 10: 777; )
787( base 4: 30103; base 10: 787; )
819( base 2: 1100110011; base 4: 30303; base 6: 3443; )
820( base 3: 1010101; base 9: 1111; )
856( base 5: 11411; base 7: 2332; )
868( base 6: 4004; base 10: 868; )
910( base 3: 1020201; base 6: 4114; base 9: 1221; )
939( base 4: 32223; base 10: 939; )
975( base 2: 1111001111; base 4: 33033; )
1023( base 2: 1111111111; base 4: 33333; )
1025( base 2: 10000000001; base 4: 100001; )
1066( base 3: 1110111; base 5: 13231; )
1105( base 2: 10001010001; base 4: 101101; )
1221( base 5: 14341; base 10: 1221; )
1285( base 2: 10100000101; base 4: 110011; )
1312( base 3: 1210121; base 7: 3553; )
1365( base 2: 10101010101; base 4: 111111; )
1432( base 5: 21212; base 7: 4114; )
1441( base 6: 10401; base 10: 1441; )
1460( base 3: 2000002; base 9: 2002; )
1539( base 2: 11000000011; base 8: 3003; )
1550( base 3: 2010102; base 9: 2112; )
1640( base 3: 2020202; base 9: 2222; )
1667( base 3: 2021202; base 5: 23132; )
1755( base 2: 11011011011; base 8: 3333; )
1885( base 4: 131131; base 6: 12421; )
2000( base 7: 5555; base 9: 2662; )
2188( base 3: 10000001; base 5: 32223; )
2268( base 5: 33033; base 8: 4334; )
2293( base 5: 33133; base 6: 14341; )
2550( base 4: 213312; base 9: 3443; )
2565( base 2: 101000000101; base 8: 5005; )
2709( base 2: 101010010101; base 5: 41314; base 8: 5225; )
2730( base 4: 222222; base 9: 3663; )
2910( base 4: 231132; base 9: 3883; )
2920( base 3: 11000011; base 9: 4004; )
2925( base 2: 101101101101; base 8: 5555; )
2997( base 7: 11511; base 8: 5665; )
3069( base 2: 101111111101; base 8: 5775; )
3074( base 5: 44244; base 6: 22122; )
3075( base 2: 110000000011; base 4: 300003; )
3280( base 3: 11111111; base 9: 4444; )
3315( base 2: 110011110011; base 4: 303303; )
3550( base 7: 13231; base 9: 4774; )
3591( base 2: 111000000111; base 8: 7007; )
3640( base 3: 11222211; base 9: 4884; )
3663( base 8: 7117; base 10: 3663; )
3735( base 2: 111010010111; base 8: 7227; )
3740( base 6: 25152; base 9: 5115; )
3855( base 2: 111100001111; base 4: 330033; )
3951( base 2: 111101101111; base 8: 7557; )
3999( base 2: 111110011111; base 6: 30303; )
4095( base 2: 111111111111; base 4: 333333; base 8: 7777; )
4097( base 2: 1000000000001; base 4: 1000001; base 8: 10001; )
4161( base 2: 1000001000001; base 4: 1001001; base 8: 10101; )
4225( base 4: 1002001; base 8: 10201; )
4257( base 2: 1000010100001; base 6: 31413; )
4289( base 4: 1003001; base 8: 10301; )
4369( base 2: 1000100010001; base 4: 1010101; )
4433( base 2: 1000101010001; base 4: 1011101; )
4593( base 2: 1000111110001; base 6: 33133; )
4617( base 2: 1001000001001; base 8: 11011; )
4681( base 2: 1001001001001; base 8: 11111; )
5001( base 6: 35053; base 8: 11611; )
5049( base 2: 1001110111001; base 7: 20502; )
5125( base 2: 1010000000101; base 4: 1100011; )
5189( base 2: 1010001000101; base 4: 1101011; )
5397( base 2: 1010100010101; base 4: 1110111; )
5461( base 2: 1010101010101; base 4: 1111111; )
5740( base 6: 42324; base 9: 7777; )
5840( base 3: 22000022; base 9: 8008; )
5854( base 6: 43034; base 7: 23032; )
6148( base 6: 44244; base 7: 23632; )
6200( base 3: 22111122; base 9: 8448; )
6560( base 3: 22222222; base 9: 8888; )
6562( base 3: 100000001; base 9: 10001; )
6643( base 2: 1100111110011; base 3: 100010001; base 9: 10101; )
6697( base 4: 1220221; base 8: 15051; )
6724( base 3: 100020001; base 9: 10201; )
6761( base 4: 1221221; base 8: 15151; )
6825( base 4: 1222221; base 8: 15251; )
6886( base 9: 10401; base 10: 6886; )
6889( base 4: 1223221; base 8: 15351; )
6953( base 7: 26162; base 8: 15451; )
7300( base 3: 101000101; base 9: 11011; )
7373( base 4: 1303031; base 6: 54045; )
7381( base 3: 101010101; base 9: 11111; )
7409( base 6: 54145; base 8: 16361; )
7447( base 2: 1110100010111; base 10: 7447; )
7462( base 3: 101020101; base 9: 11211; )
7517( base 4: 1311131; base 6: 54445; )
7667( base 6: 55255; base 10: 7667; )
7703( base 6: 55355; base 7: 31313; )
7777( base 6: 100001; base 10: 7777; )
7801( base 7: 31513; base 8: 17171; )
7997( base 4: 1330331; base 10: 7997; )
8038( base 3: 102000201; base 9: 12021; )
8119( base 3: 102010201; base 9: 12121; )
8194( base 4: 2000002; base 8: 20002; )
8200( base 3: 102020201; base 7: 32623; base 9: 12221; )
8258( base 4: 2001002; base 8: 20102; )
8281( base 6: 102201; base 9: 12321; )
8322( base 4: 2002002; base 8: 20202; )
8386( base 4: 2003002; base 8: 20302; )
8578( base 3: 102202201; base 8: 20602; )
8778( base 8: 21112; base 10: 8778; )
8802( base 4: 2021202; base 7: 34443; )
9009( base 2: 10001100110001; base 10: 9009; )
9103( base 3: 110111011; base 7: 35353; )
9201( base 2: 10001111110001; base 7: 35553; )
9222( base 4: 2100012; base 5: 243342; )
9490( base 3: 111000111; base 8: 22422; )
9958( base 4: 2123212; base 7: 41014; )

 

 

 

 

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