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A272670 Numbers whose binary expansion is not palindromic but which when reversed and leading zeros omitted, does form a palindrome.

%I A272670 #19 May 21 2016 13:38:06
%S A272670 2,4,6,8,10,12,14,16,18,20,24,28,30,32,34,36,40,42,48,54,56,60,62,64,
%T A272670 66,68,72,80,84,90,96,102,108,112,120,124,126,128,130,132,136,144,146,
%U A272670 160,168,170,180,186,192,198,204,214,216,224,238,240,248,252,254
%N A272670 Numbers whose binary expansion is not palindromic but which when reversed and leading zeros omitted, does form a palindrome.
%C A272670 Decimal interpretation of A273245. Twice A057890.
%H A272670 Chai Wah Wu, <a href="/A272670/b272670.txt">Table of n, a(n) for n = 1..10000</a>
%p A272670 isPal := proc(L::list)
%p A272670     local i;
%p A272670     for i from 1 to nops(L)/2 do
%p A272670         if op(i,L) <> op(-i,L) then
%p A272670             return false;
%p A272670         end if;
%p A272670     end do:
%p A272670     true ;
%p A272670 end proc:
%p A272670 isA272670 := proc(n)
%p A272670     local bdgs ;
%p A272670     bdgs := convert(n,base,2) ;
%p A272670     if isPal(bdgs) then
%p A272670         return false;
%p A272670     else
%p A272670         A000265(n) ;
%p A272670         bdgs := convert(%,base,2) ;
%p A272670         isPal(bdgs) ;
%p A272670     end if;
%p A272670 end proc:
%p A272670 for n from 1 to 500 do
%p A272670     if isA272670(n) then
%p A272670         printf("%d,",n) ;
%p A272670     end if;
%p A272670 end do: # _R. J. Mathar_, May 20 2016
%o A272670 (Python)
%o A272670 A272670_list = [n for n in range(1,10**4) if bin(n)[2:] != bin(n)[:1:-1] and bin(n)[2:].rstrip('0') == bin(n)[:1:-1].lstrip('0')] # _Chai Wah Wu_, May 21 2016
%Y A272670 Cf. A006995, A057890, A273245, A273329, subsequence of A154809.
%K A272670 nonn,base,easy
%O A272670 1,1
%A A272670 _N. J. A. Sloane_, May 19 2016