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%I #18 Apr 08 2023 10:09:52
%S 15,17,27,29,30,34,36,43,45,51,54,57,58,60,63,68,71,72,75,85,86,90,92,
%T 102,108,113,114,126,129,132,135,139,144,147,150,159,165,170,175,177,
%U 192,195,197,198,201,204,210,216,219,226,228,231,237,264,270,288,291
%N Nonpalindromic integers which have an even number of ones in binary and whose reverse does as well.
%H Robert Israel, <a href="/A091017/b091017.txt">Table of n, a(n) for n = 1..10000</a>
%e 15 is a term because 15_10 = 1111_2 has 4 1's and 51_10 = 110011_2 also has 4 1's.
%p filter:= proc(n) local L,r,j;
%p L:= convert(n,base,10);
%p r:= add(L[-j]*10^(j-1),j=1..nops(L));
%p r <> n and convert(convert(n,base,2),`+`)::even and convert(convert(r,base,2),`+`)::even
%p end proc:
%p select(filter, [$1..1000]); # _Robert Israel_, May 11 2021
%t Reveral[n_] := FromDigits[ Reverse[ IntegerDigits[ n]]]; Select[ Range[ 296], Reveral[ # ] != # && EvenQ[ Count[ IntegerDigits[ #, 2], 1]] && EvenQ[ Count[ IntegerDigits[ Reveral[ # ], 2], 1]] &] (* _Robert G. Wilson v_, Feb 26 2004 *)
%t npeoQ[n_]:=!PalindromeQ[n]&&AllTrue[{DigitCount[n,2,1],DigitCount[ IntegerReverse[ n],2,1]},EvenQ]; Select[Range[300],npeoQ] (* _Harvey P. Dale_, Apr 08 2023 *)
%Y Cf. A006567, A001969, A000040.
%K easy,nonn,base
%O 1,1
%A _Michael Joseph Halm_, Feb 25 2004
%E Edited, corrected and extended by _Robert G. Wilson v_, Feb 26 2004
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