A340559 Numbers that are palindromic in base 2 and base 16.

0, 1, 3, 5, 7, 9, 15, 17, 51, 85, 119, 153, 255, 257, 273, 771, 819, 1285, 1317, 1365, 1397, 1799, 1831, 1879, 1911, 2313, 2409, 2457, 2553, 3855, 3951, 3999, 4095, 4097, 4369, 12291, 13107, 20485, 21029, 21845, 22389, 28679, 29223, 30039, 30583, 36873, 38505

Offset: 1

Author

Glen Gilchrist, Jan 11 2021

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A006995 and A029730.

Cf. A029731, A007632.

Programs

Mathematica

Select[Range[0, 10^5], PalindromeQ @ IntegerDigits[#, 2] && PalindromeQ @ IntegerDigits[#, 16]  &] (* Amiram Eldar, Jan 11 2021 *)

PARI

ispal(m, b) = my(d=digits(m, b)); d == Vecrev(d);
isok(m) = ispal(m, 2) && ispal(m, 16); \\ Michel Marcus, Jan 20 2021

Python

def palindrome(x):
    res = str(x) == str(x)[::-1]
    return res
def dec_to_bin(x):
    return int(bin(x)[2:])
def dec_to_hex(x):
    return (hex(x)[2:])
for x in range (1,10000):
    if palindrome(dec_to_hex(x)) & palindrome(dec_to_bin(x)) == True:
          print(x)
(BASIC:- MM Basic, a modern QBASIC variant, https://www.mmbasic.com/)
Function reverse(in_string$) As string
  Local r$
  Local i
  For i = Len(in_string$) To 1 Step -1
      b$=Mid$(in_string$,i,1)
      r$=r$+b$
  Next i
  reverse=r$
End Function
For i = 1 To 10000
  If Bin$(i) = reverse(Bin$(i)) Then
      If Hex$(i) = reverse(Hex$(i)) Then
          Print i,Bin$(i), Hex$(i)
      EndIf
  EndIf
Next i