A124334 - OEIS

%I #13 Nov 10 2024 15:18:51

%S 15,17,21,27,31,45,51,63,65,73,85,93,107,119,127,129,153,165,189,195,

%T 219,231,255,257,273,297,325,341,365,381,387,403,427,443,455,471,495,

%U 511,513,561,633,645,693,765,771,819,843,891,903,951,975

%N Nonpalindromes in base 10 that are palindromes in base 2.

%H Robert Israel, <a href="/A124334/b124334.txt">Table of n, a(n) for n = 1..10000</a>

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

%p N:= 10000: # to get the first N entries

%p count:= 0:

%p for d from 1 while count < N do

%p    d1:= ceil(d/2); d2:= d - d1;

%p    for x from 2^(d1-1) to 2^d1 - 1 while count < N do

%p       if d::even then x1:= x else x1 := floor(x/2) fi;

%p       L:= convert(x1,base,2);

%p       y:= 2^(d2)*x + add(L[j]*2^(d2-j),j=1..d2);

%p       L10:= convert(y,base,10);

%p       if ListTools[Reverse](L10) = L10 then next fi;

%p       count:= count+1;

%p       A[count]:= y;

%p    od

%p od:

%p seq(A[n],n=1..N);

%p # _Robert Israel_, Apr 20 2014

%t Select[Range[1000], Reverse[IntegerDigits[ # ]] != IntegerDigits[ # ] && Reverse[IntegerDigits[ #, 2]] == IntegerDigits[ #, 2] &]

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

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

%K base,nonn

%O 1,1

%A _Tanya Khovanova_, Dec 26 2006