A091017 Nonpalindromic integers which have an even number of ones in binary and whose reverse does as well.

15, 17, 27, 29, 30, 34, 36, 43, 45, 51, 54, 57, 58, 60, 63, 68, 71, 72, 75, 85, 86, 90, 92, 102, 108, 113, 114, 126, 129, 132, 135, 139, 144, 147, 150, 159, 165, 170, 175, 177, 192, 195, 197, 198, 201, 204, 210, 216, 219, 226, 228, 231, 237, 264, 270, 288, 291

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

15 is a term because 15_10 = 1111_2 has 4 1's and 51_10 = 110011_2 also has 4 1's.

Maple

filter:= proc(n) local L, r, j;
  L:= convert(n, base, 10);
  r:= add(L[-j]*10^(j-1), j=1..nops(L));
  r <> n and convert(convert(n, base, 2), `+`)::even  and convert(convert(r, base, 2), `+`)::even
end proc:
select(filter, [$1..1000]); # Robert Israel, May 11 2021

Mathematica

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 *)
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 *)

Crossrefs

Cf. A006567, A001969, A000040.

Sequence in context: A002155 A290749 A374005 * A157716 A113968 A093812

Adjacent sequences: A091014 A091015 A091016 * A091018 A091019 A091020

Keyword

easy,nonn,base

Author

Michael Joseph Halm, Feb 25 2004

Extensions

Edited, corrected and extended by Robert G. Wilson v, Feb 26 2004

Status

approved