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A091017
Nonpalindromic integers which have an even number of ones in binary and whose reverse does as well.
1
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
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
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