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

1,3

Links

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

Mathematica

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

Prog

(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
(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

Crossrefs

Intersection of A006995 and A029730.

Cf. A029731, A007632.

Sequence in context: A265852 A335132 A343727 * A073674 A084722 A083566

Adjacent sequences: A340556 A340557 A340558 * A340560 A340561 A340562

Keyword

nonn,base

Author

Glen Gilchrist, Jan 11 2021

Status

approved