A265543 a(n) = smallest base-2 palindrome m >= n such that every base-2 digit of n is <= the corresponding digit of m; m is written in base 2.

0, 1, 11, 11, 101, 101, 111, 111, 1001, 1001, 1111, 1111, 1111, 1111, 1111, 1111, 10001, 10001, 11011, 11011, 10101, 10101, 11111, 11111, 11011, 11011, 11011, 11011, 11111, 11111, 11111, 11111, 100001, 100001, 110011, 110011, 101101, 101101, 111111, 111111, 101101, 101101, 111111, 111111, 101101, 101101, 111111

Offset: 0

Author

N. J. A. Sloane, Dec 09 2015

Keywords

• nonn
• base

Crossrefs

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.

See A206913 for the values of m written in base 10.

Programs

Maple

ispal:= proc(n) global b; # test if n is base-b palindrome
  local L, Ln, i;
  L:= convert(n, base, b);
  Ln:= nops(L);
for i from 1 to floor(Ln/2) do
if L[i] <> L[Ln+1-i] then return(false); fi;
od:
return(true);
end proc;
# find min pal >= n and with n in base-b shadow, write in base 10
over10:=proc(n) global b;
local t1,t2,i,m,sw1,L1;
t1:=convert(n,base,b);
L1:=nops(t1);
for m from n to 10*n do
if ispal(m) then
   t2:=convert(m,base,b);
   sw1:=1;
   for i from 1 to L1 do
      if t1[i] > t2[i] then sw1:=-1; break; fi;
                      od:
   if sw1=1 then return(m); fi;
fi;
                       od;
lprint("no solution in over10 for n = ", n);
end proc;
# find min pal >= n and with n in base-b shadow, write in base 10
overb:=proc(n) global b;
local t1,t2,i,m,mb,sw1,L1;
t1:=convert(n,base,b);
L1:=nops(t1);
for m from n to 10*n do
if ispal(m) then
   t2:=convert(m,base,b);
   sw1:=1;
   for i from 1 to L1 do
      if t1[i] > t2[i] then sw1:=-1; break; fi;
                      od:
   if sw1=1 then mb:=add(t2[i]*10^(i-1), i=1..nops(t2)); return(mb); fi;
fi;
                       od;
lprint("no solution in over10 for n = ", n);
end proc;
b:=2;
[seq(over10(n),n=0..144)]; # A175298
[seq(overb(n),n=0..144)]; # A265543

Mathematica

sb2p[n_]:=Module[{m=n},While[!PalindromeQ[IntegerDigits[m,2]]|| Min[ IntegerDigits[ m,2]-IntegerDigits[n,2]]<0,m++];FromDigits[ IntegerDigits[ m,2]]]; Array[sb2p,50,0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 15 2017 *)