cp's OEIS Frontend

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

%I A176630 #15 Apr 08 2025 21:55:32
%S A176630 92,732,759,957,5485,5845,71869,77360,96817,319773,377913,13162800,
%T A176630 39781062,79497594,94729789,98792749,144579540,1231493321,1233941321,
%U A176630 7075293947,7493925707,32817543720,71461803829,92830816417,169709554740,1432254694771,1774964522341
%N A176630 Nonpalindromic numbers whose binary representation when reversed is the same as binary representation of the number reversed in decimal.
%C A176630 The binary representation of a decimal number, when reversed, is also the reverse of the decimal number.
%F A176630 Intersection of A029742 and A081434. - _Andrew Howroyd_, Jan 14 2020
%e A176630 92 = 1011100 mirrors 0011101 = 29.
%e A176630 732 = 1011011100 mirrors 0011101101 = 237.
%t A176630 Select[Range[10^6], And[! PalindromeQ@ #, Drop[#, LengthWhile[#, # == 0 &]] &@ Reverse@ IntegerDigits[#, 2] === IntegerDigits[IntegerReverse[#], 2]] &] (* _Michael De Vlieger_, Dec 29 2020 *)
%o A176630 (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
%o A176630 (Python)
%o A176630 def agen():
%o A176630   k = 0
%o A176630   while True:
%o A176630     strk = str(k)
%o A176630     revstrk = strk[::-1]
%o A176630     if revstrk != strk:
%o A176630       if int(revstrk) == int((bin(k)[2:])[::-1], 2):
%o A176630         yield k
%o A176630     k += 1
%o A176630 g = agen()
%o A176630 print([next(g) for i in range(11)]) # _Michael S. Branicky_, Dec 29 2020
%Y A176630 Cf. A029742, A081434.
%K A176630 nonn,base
%O A176630 1,1
%A A176630 _Gil Broussard_, Apr 22 2010
%E A176630 Name clarified and a(12)-a(17) from _Andrew Howroyd_, Jan 14 2020
%E A176630 a(18)-a(24) from _Michael S. Branicky_, Dec 29 2020
%E A176630 a(25)-a(27) from _Jinyuan Wang_, Apr 07 2025