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A124334 Nonpalindromes in base 10 that are palindromes in base 2.

%I A124334 #13 Nov 10 2024 15:18:51
%S A124334 15,17,21,27,31,45,51,63,65,73,85,93,107,119,127,129,153,165,189,195,
%T A124334 219,231,255,257,273,297,325,341,365,381,387,403,427,443,455,471,495,
%U A124334 511,513,561,633,645,693,765,771,819,843,891,903,951,975
%N A124334 Nonpalindromes in base 10 that are palindromes in base 2.
%H A124334 Robert Israel, <a href="/A124334/b124334.txt">Table of n, a(n) for n = 1..10000</a>
%e A124334 17(10) = 10001(2), a palindrome.
%p A124334 N:= 10000: # to get the first N entries
%p A124334 count:= 0:
%p A124334 for d from 1 while count < N do
%p A124334    d1:= ceil(d/2); d2:= d - d1;
%p A124334    for x from 2^(d1-1) to 2^d1 - 1 while count < N do
%p A124334       if d::even then x1:= x else x1 := floor(x/2) fi;
%p A124334       L:= convert(x1,base,2);
%p A124334       y:= 2^(d2)*x + add(L[j]*2^(d2-j),j=1..d2);
%p A124334       L10:= convert(y,base,10);
%p A124334       if ListTools[Reverse](L10) = L10 then next fi;
%p A124334       count:= count+1;
%p A124334       A[count]:= y;
%p A124334    od
%p A124334 od:
%p A124334 seq(A[n],n=1..N);
%p A124334 # _Robert Israel_, Apr 20 2014
%t A124334 Select[Range[1000], Reverse[IntegerDigits[ # ]] != IntegerDigits[ # ] && Reverse[IntegerDigits[ #, 2]] == IntegerDigits[ #, 2] &]
%t A124334 pal2[n_]:=With[{c=IntegerDigits[n,2]},c==Reverse[c]]; Select[Range[1000],!PalindromeQ[#]&&pal2[#]&] (* _Harvey P. Dale_, Nov 10 2024 *)
%Y A124334 Cf. A007632 = numbers that are palindromic in bases 2 and 10.
%K A124334 base,nonn
%O A124334 1,1
%A A124334 _Tanya Khovanova_, Dec 26 2006