A176630 Nonpalindromic numbers whose binary representation when reversed is the same as binary representation of the number reversed in decimal.

92, 732, 759, 957, 5485, 5845, 71869, 77360, 96817, 319773, 377913, 13162800, 39781062, 79497594, 94729789, 98792749, 144579540, 1231493321, 1233941321, 7075293947, 7493925707, 32817543720, 71461803829, 92830816417, 169709554740, 1432254694771, 1774964522341

Offset: 1

Author

Gil Broussard, Apr 22 2010

Keywords

• nonn
• base

Comments

The binary representation of a decimal number, when reversed, is also the reverse of the decimal number.

Examples

			92 = 1011100 mirrors 0011101 = 29.
732 = 1011011100 mirrors 0011101101 = 237.
		

Crossrefs

Cf. A029742, A081434.

Programs

Mathematica

Select[Range[10^6], And[! PalindromeQ@ #, Drop[#, LengthWhile[#, # == 0 &]] &@ Reverse@ IntegerDigits[#, 2] === IntegerDigits[IntegerReverse[#], 2]] &] (* Michael De Vlieger, Dec 29 2020 *)

PARI

is(k)={my(t=fromdigits(Vecrev(digits(k,10)),10)); t<>k && t == fromdigits(Vecrev(digits(k,2)),2)} \\ Andrew Howroyd, Jan 14 2020

Python

def agen():
  k = 0
  while True:
    strk = str(k)
    revstrk = strk[::-1]
    if revstrk != strk:
      if int(revstrk) == int((bin(k)[2:])[::-1], 2):
        yield k
    k += 1
g = agen()
print([next(g) for i in range(11)]) # Michael S. Branicky, Dec 29 2020

Formula

Intersection of A029742 and A081434. - Andrew Howroyd, Jan 14 2020

Extensions

Name clarified and a(12)-a(17) from Andrew Howroyd, Jan 14 2020

a(18)-a(24) from Michael S. Branicky, Dec 29 2020

a(25)-a(27) from Jinyuan Wang, Apr 07 2025