A265526 Largest base-2 palindrome m <= n, written in base 2.

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

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Maple

ispal:= proc(n) global b; # test for 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 max pal <= n, write in base 10
less10:=proc(n) global b;
local t1, t2, i, m, sw1, L2;
t1:=convert(n, base, b);
for m from n by -1 to 0 do
if ispal(m) then return(m); fi;
                        od;
end proc;
# find max pal <= n, write in base b
lessb:=proc(n) global b;
local t1, t2, i, m, mb, sw1, L2;
t1:=convert(n, base, b);
for m from n by -1 to 0 do
if ispal(m) then
   t2:=convert(m, base, b);
   L2:=nops(t2);
   mb:=add(t2[i]*10^(i-1), i=1..L2); return(mb); fi;
                        od;
end proc;
b:=2;
[seq(less10(n), n=0..100)]; # A206913
[seq(lessb(n), n=0..100)]; # A265526
[seq(less10(2*n), n=0..100)]; # A265527
[seq(lessb(2*n), n=0..100)]; # A265528
b:=10;
[seq(less10(n), n=0..100)]; # A261423

Crossrefs

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

Sequence in context: A243127 A088761 A215256 * A265559 A265543 A062128

Adjacent sequences: A265523 A265524 A265525 * A265527 A265528 A265529

Keyword

nonn,base

Author

N. J. A. Sloane, Dec 09 2015

Status

approved