project_euler_36.md

The decimal number, 585 = 1001001001 base2 (binary), is palindromic in both bases.

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

(Please note that the palindromic number, in either base, may not include leading zeros.)

format(585, 'b')

'1001001001'

'civic' == 'civic'[::-1]

True

[1,2,3][::-1]

[3, 2, 1]

def conv_bin(number):
    return format(number, 'b')

def is_pal(string):
    return string == string[::-1]

vals = list(range(1000000))
vals[-1]

999999

pairs = {str(x) : conv_bin(x) for x in vals}
pairs['585']

'1001001001'

good_ones = {}

for k, v in pairs.items():
    if is_pal(k) and is_pal(v):
        good_ones[k] = v

len(pairs.keys())

1000000

len(good_ones.keys())

20

good_ones

{'0': '0',
 '1': '1',
 '15351': '11101111110111',
 '3': '11',
 '313': '100111001',
 '32223': '111110111011111',
 '33': '100001',
 '39993': '1001110000111001',
 '5': '101',
 '53235': '1100111111110011',
 '53835': '1101001001001011',
 '585': '1001001001',
 '585585': '10001110111101110001',
 '7': '111',
 '717': '1011001101',
 '73737': '10010000000001001',
 '7447': '1110100010111',
 '9': '1001',
 '9009': '10001100110001',
 '99': '1100011'}

sum(list(map(int, list(good_ones.keys()))))

872187