A253147 -id:A253147 - cp's OEIS frontend

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

Chai Wah Wu, Dec 30 2014

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

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

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

Cf. A253147, A253149, A238853.

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

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)

Name clarified by Tanya Khovanova, Aug 21 2021

A253149 Primes >= 256 that remain primes when the digits are reversed in base 256.

Original entry on oeis.org

257, 269, 293, 311, 313, 347, 379, 397, 419, 449, 479, 491, 773, 809, 823, 827, 829, 857, 883, 887, 947, 953, 971, 977, 1013, 1283, 1289, 1297, 1301, 1307, 1321, 1327, 1367, 1373, 1399, 1409, 1429, 1439, 1451, 1453, 1481, 1483, 1511, 1523, 1801, 1811, 1847, 1867

Offset: 1

Chai Wah Wu, Dec 30 2014

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.

			1299647 is prime and written in base 16 is 13 d4 bf whereas bf d4 13 = 12571667 is also prime.

Chai Wah Wu, Table of n, a(n) for n = 1..7110
Wikipedia, Endianness

Cf. A253147, A253148, A238853.

from sympy import prime, isprime
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
A253149_list = []
for n in range(1, 300):
    p = prime(n)
    if p > 255 and isprime(reversedigits(p,256)):
        A253149_list.append(p)
print(A253149_list)

cp's OEIS Frontend

A253148 Nontrivial palindromes in base 10 and base 256.

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