A253147 Palindromes in base 10 >= 256 that remain palindromes when the digits are reversed in base 256.

8448, 31613, 32123, 55255, 63736, 92929, 96769, 108801, 450054, 516615, 995599, 1413141, 1432341, 1539351, 1558551, 2019102, 2491942, 2513152, 2712172, 2731372, 2750572, 2807082, 2838382, 2857582, 2876782, 3097903, 3740473, 3866683, 3885883, 4201024, 4220224, 4327234

Offset

1,1

Comments

Reversing the digits in base 256 is equivalent to reading a number in big-endian format using little-endian order with 8-bit words. See also A238853.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..176

Wikipedia, Endianness

Example

2857582 is in the sequence since 2857582 is 2b 9a 6e in base 16 and 6e 9a 2b = 7248427 is a palindrome.

Prog

(Python)
def palgen(l, b=10): # generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, l+1):
            n = b**(x-1)
            n2 = n*b
            for y in range(n, n2):
                k, m = y//b, 0
                while k >= b:
                    k, r = divmod(k, b)
                    m = b*m + r
                yield y*n + b*m + k
            for y in range(n, n2):
                k, m = y, 0
                while k >= b:
                    k, r = divmod(k, b)
                    m = b*m + r
                yield y*n2 + b*m + k
def reversedigits(n, b=10): # reverse digits of n in base b
    x, y = n, 0
    while x >= b:
        x, r = divmod(x, b)
        y = b*y + r
    return b*y + x
A253147_list = []
for n in palgen(4):
    x = reversedigits(n, 256)
    if n > 255 and x == reversedigits(x, 10):
        A253147_list.append(n)

Crossrefs

Cf. A253148, A253149, A238853.

Sequence in context: A116258 A116311 A116351 * A046336 A046384 A170787

Adjacent sequences: A253144 A253145 A253146 * A253148 A253149 A253150

Keyword

nonn,base

Author

Chai Wah Wu, Dec 29 2014

Status

approved