A253148 Nontrivial palindromes in base 10 and base 256.

55255, 63736, 92929, 96769, 108801, 450054, 516615, 995599, 1413141, 1432341, 1539351, 1558551, 2019102, 2491942, 2807082, 3097903, 3740473, 3866683, 3885883, 4201024, 4220224, 4327234, 4346434, 4365634, 4384834, 5614165, 5633365, 5759575, 6692966, 7153517, 7172717

Offset: 1

Author

Chai Wah Wu, Dec 30 2014

Keywords

• nonn
• base

Comments

Palindromes in base 256 are numbers that are the same in big-endian and little-endian order with 8-bit words. See also A238853.

A palindromic number in base 10 which is below 256 is a 1-digit number in base 256. Thus, it is automatically a palindrome in base 256. This sequence excludes 1-digit numbers in base 256. - Tanya Khovanova, Aug 21 2021

Examples

			7172717 in base 16 is 6d 72 6d and the bytes form a palindrome.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..121
• Wikipedia, Endianness

Crossrefs

Cf. A253147, A253149, A238853.

Programs

Mathematica

Select[Range[256, 10000000], PalindromeQ[#] && PalindromeQ[IntegerDigits[#, 256]] &] (* Tanya Khovanova, Aug 21 2021 *)

Python

from _future_ import division
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
A253148_list = []
for n in palgen(5):
    if n > 255 and n == reversedigits(n,256):
        A253148_list.append(n)

Extensions

Name clarified by Tanya Khovanova, Aug 21 2021