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

1,1

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

Links

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

Wikipedia, Endianness

Example

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

Mathematica

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

Prog

(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)

Crossrefs

Cf. A253147, A253149, A238853.

Sequence in context: A237732 A251164 A383129 * A204776 A237485 A092008

Adjacent sequences: A253145 A253146 A253147 * A253149 A253150 A253151

Keyword

nonn,base

Author

Chai Wah Wu, Dec 30 2014

Extensions

Name clarified by Tanya Khovanova, Aug 21 2021

Status

approved