This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(6)=6 because 0110 is a palindrome, but a(11)=13 because 1011 reverses into 1101.
Table[FromDigits[Reverse[IntegerDigits[n, 2]], 2]*2^IntegerExponent[n, 2], {n, 71}] (* Ivan Neretin, Jul 09 2015 *)
A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2)); A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2))); \\ Antti Karttunen, Dec 25 2024
def a(n):
x = bin(n)[2:]
y = x[::-1]
return int(str(int(y))+(len(x) - len(str(int(y))))*'0', 2)
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 11 2017
def A057889(n): return int(bin(n>>(m:=(~n&n-1).bit_length()))[-1:1:-1],2)<Chai Wah Wu, Dec 25 2024
10 is included, since 01010 is a palindrome, but 11 is not because 1011 is not.
a057890 n = a057890_list !! (n-1) a057890_list = 0 : filter ((== 1) . a178225 . a000265) [1..] -- Reinhard Zumkeller, Oct 21 2011
dmax:= 10: # to get all terms < 2^dmax
revdigs:= proc(n)
local L, Ln, i;
L:= convert(n, base, 2);
Ln:= nops(L);
add(L[i]*2^(Ln-i), i=1..Ln);
end proc;
P[0]:= {0}:
P[1]:= {1}:
for d from 2 to dmax do
if d::even then
P[d]:= { seq(2^(d/2)*x + revdigs(x), x=2^(d/2-1)..2^(d/2)-1)}
else
m:= (d-1)/2;
B:={seq(2^(m+1)*x + revdigs(x), x=2^(m-1)..2^m-1)};
P[d]:= B union map(`+`, B, 2^m)
fi
od:
A:= `union`(seq(seq(map(`*`,P[d],2^k),k=0..dmax-d),d=0..dmax)):
sort(convert(A,list)); # Robert Israel, Jun 07 2016
PaleQ[n_Integer, base_Integer] := Module[{idn, trim = n/base^IntegerExponent[n, base]}, idn = IntegerDigits[trim, base]; idn == Reverse[idn]]; Select[Range[0, 150], PaleQ[#, 2] &] (* Lei Zhou, Dec 13 2013 *)
pal2Q[n_]:=Module[{id=Drop[IntegerDigits[n,2],-IntegerExponent[n,2]]},id==Reverse[id]]; Join[{0},Select[Range[200],pal2Q]] (* Harvey P. Dale, Feb 26 2015 *)
A057890Q = If[# > 0 && EvenQ@#, #0[#/2], # == #~IntegerReverse~2] &; Select[0~Range~146, A057890Q] (* JungHwan Min, Mar 29 2017 *)
Select[Range[0, 200], PalindromeQ[IntegerDigits[#, 2] /. {b__, 0..} -> {b} ]&] (* Jean-François Alcover, Sep 18 2018 *)
bitrev(n) = subst(Pol(Vecrev(binary(n>>valuation(n,2))), 'x), 'x, 2); is(n) = my(x = n >> valuation(n,2)); x == bitrev(x); concat(0, select(is,vector(147,n,n))) \\ Gheorghe Coserea, Jun 07 2016
is(n)=n==0 || Vecrev(n=binary(n>>valuation(n,2)))==n \\ Charles R Greathouse IV, Aug 25 2016
A057890 = [n for n in range(10**6) if bin(n)[2:].rstrip('0') == bin(n)[2:].rstrip('0')[::-1]] # Chai Wah Wu, Aug 12 2014
a061917 n = a061917_list !! (n-1)
a061917_list = filter chi [0..] where
chi x = zs == reverse zs where
zs = dropWhile (== '0') $ reverse $ show x
-- Reinhard Zumkeller, Sep 25 2011
PaleQ[n_Integer, base_Integer] := Module[{idn, trim = n/base^IntegerExponent[n, base]}, idn = IntegerDigits[trim, base]; idn == Reverse[idn]]; Select[Range[0, 500], PaleQ[#, 10] &] (* Lei Zhou, Dec 13 2013 *)
Join[{0},Select[Range[500],PalindromeQ[FromDigits[Drop[IntegerDigits[#],-IntegerExponent[#,10]]]]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 27 2017 *)
isOK(k)=k==0||fromdigits(Vecrev(digits(k)))==k/10^valuation(k,10) \\ Jeppe Stig Nielsen, Jan 17 2022
def ispal(s): return s == s[::-1]
def ok(n): s = str(n); return ispal(s) or ispal(s.rstrip('0'))
print([k for k in range(405) if ok(k)]) # Michael S. Branicky, Jan 17 2022
Table[If[IntegerDigits[n,2]==Reverse[IntegerDigits[n,2]],0,1],{n,0,120}] (* Harvey P. Dale, Aug 07 2023 *)
A178226(n) = (n!=subst(Polrev(binary(n)),x,2)); \\ Antti Karttunen, Dec 15 2017
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