A253147 - OEIS

%I #13 Nov 02 2024 16:02:29

%S 8448,31613,32123,55255,63736,92929,96769,108801,450054,516615,995599,

%T 1413141,1432341,1539351,1558551,2019102,2491942,2513152,2712172,

%U 2731372,2750572,2807082,2838382,2857582,2876782,3097903,3740473,3866683,3885883,4201024,4220224,4327234

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

%C 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.

%H Chai Wah Wu, <a href="/A253147/b253147.txt">Table of n, a(n) for n = 1..176</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Endianness">Endianness</a>

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

%o (Python)

%o def palgen(l, b=10): # generator of palindromes in base b of length <= 2*l

%o     if l > 0:

%o         yield 0

%o         for x in range(1, l+1):

%o             n = b**(x-1)

%o             n2 = n*b

%o             for y in range(n, n2):

%o                 k, m = y//b, 0

%o                 while k >= b:

%o                     k, r = divmod(k, b)

%o                     m = b*m + r

%o                 yield y*n + b*m + k

%o             for y in range(n, n2):

%o                 k, m = y, 0

%o                 while k >= b:

%o                     k, r = divmod(k, b)

%o                     m = b*m + r

%o                 yield y*n2 + b*m + k

%o def reversedigits(n, b=10): # reverse digits of n in base b

%o     x, y = n, 0

%o     while x >= b:

%o         x, r = divmod(x, b)

%o         y = b*y + r

%o     return b*y + x

%o A253147_list = []

%o for n in palgen(4):

%o     x = reversedigits(n, 256)

%o     if n > 255 and x == reversedigits(x, 10):

%o         A253147_list.append(n)

%Y Cf. A253148, A253149, A238853.

%K nonn,base

%O 1,1

%A _Chai Wah Wu_, Dec 29 2014