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

15, 17, 21, 27, 31, 45, 51, 63, 65, 73, 85, 93, 107, 119, 127, 129, 153, 165, 189, 195, 219, 231, 255, 257, 273, 297, 325, 341, 365, 381, 387, 403, 427, 443, 455, 471, 495, 511, 513, 561, 633, 645, 693, 765, 771, 819, 843, 891, 903, 951, 975

Offset: 1

Author

Tanya Khovanova, Dec 26 2006

Keywords

• base
• nonn

Examples

			17(10) = 10001(2), a palindrome.
		

Links

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

Crossrefs

Cf. A007632 = numbers that are palindromic in bases 2 and 10.

Programs

Maple

N:= 10000: # to get the first N entries
count:= 0:
for d from 1 while count < N do
   d1:= ceil(d/2); d2:= d - d1;
   for x from 2^(d1-1) to 2^d1 - 1 while count < N do
      if d::even then x1:= x else x1 := floor(x/2) fi;
      L:= convert(x1,base,2);
      y:= 2^(d2)*x + add(L[j]*2^(d2-j),j=1..d2);
      L10:= convert(y,base,10);
      if ListTools[Reverse](L10) = L10 then next fi;
      count:= count+1;
      A[count]:= y;
   od
od:
seq(A[n],n=1..N);
# Robert Israel, Apr 20 2014

Mathematica

Select[Range[1000], Reverse[IntegerDigits[ # ]] != IntegerDigits[ # ] && Reverse[IntegerDigits[ #, 2]] == IntegerDigits[ #, 2] &]
pal2[n_]:=With[{c=IntegerDigits[n,2]},c==Reverse[c]]; Select[Range[1000],!PalindromeQ[#]&&pal2[#]&] (* Harvey P. Dale, Nov 10 2024 *)